'It's a wonderful thing to have closure.' Uma Thurman wins primary custody of her daughter after a bitter legal battle with financier ex Arpad Busson

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The bitter custody battle fought by Uma Thurman and her multimillionaire ex-fiancé has been settled.

Eleanor Alter, Thurman's lawyer, confirmed that the actress won primary custody of their four-year-old daughter, Luna. 

Thurman, 46, briefly appeared in court on Friday morning with her attorneys to confirm that she agreed with the terms of the settlement with Arpad Busson.

Manhattan Supreme Justice Matthew Cooper formally allocuted the Oscar-nominated star to make sure she understood the process. Cooper asked the actress if she had read the 38-page agreement in its entirety and if she agreed to it.

'Yes,' she replied.

Cooper then asked: 'Are you under the influence of any medication that might influence your decision?'

Uma Thurman arrives to court today to sign off on the custody agreement she reached with her ex Arpad Busson over their four-year-old daughter, Luna. Busson is not in court today

The mother-daughter duo enjoyed a girls night out on Wednesday, attending the Cirque du Soleil show, Paramour,  in New York City

Thuman and Luna watched as the performers showed off their impressive moves

Uma Thurman's ex-fiancé Arpad Busson showed up in court Thursday to sign off on the custody agreement over their daughter but the actress went to a reading for a Broadway play

'No,' Thurman answered.

The judge told Thurman that he was delighted that the parents had come to an agreement on how to raise their daughter and that he would not need to make a decision. He also made clear that their agreement would carry the same legal weight as a decision made by him.

Cooper said: 'The agreement is so ordered and I am pleased we have reached a resolution in this matter. It is an excellent thing for the court, the lawyers, for both parties and most of all, the child.

'Luna has all the advantages in life, two parents who love her and provide amply for her. She has every opportunity to be culturally and educationally enriched and to be loved by her parents and brothers and sisters.'

He added: 'The only thing that is lacking, and I hope is forthcoming, is that her parents can reach some kind of place where they can put aside their anger and are able to cooperate… If parents can work together collectively, then she will have everything that any child could want in life.'

Thurman profusely thanked the judge and the trial was concluded.

The actress, dressed sharply in a black suit with white shirt, smiled broadly as she left court. She said: 'It's a wonderful thing to have closure.'

When asked whether she thought the judge's request that the parents reach an amicable relationship was possible, she replied: 'Hope springs eternal.'

Thurman was all smiles as she arrived to Manhattan Supreme Court on Friday

Thurman's lawyers, Eleanor Alter and Adam Wolff, would not comment but smiled and appeared pleased with the decision on leaving court.

Busson did not attend the court appearance on Friday and was believed to have boarded a flight to London.

He was represented on Friday by one of his attorneys, Eric Buckley.

Busson was formally allocated by the judge on Thursday where he confirmed his agreement to the settlement.

The pair had agreed to a tentative settlement at the court hearing on Thursday which Thurman, 46, did not attend because she was too busy at a reading for a play, The Parisian Woman. 

She said on Friday that she was playing the eponymous role in the Broadway production. 

But Thurman's attorney Eleanor Alter confirmed her agreement over the phone to the judge and later went to a Broadway studio so Thurman could sign the paperwork. 

It brings to an end the rancorous two-year battle between Thurman and 53-year-old Busson over how and where their little girl, Luna, should be raised. 

The details of the agreement have not been made public. Thurman and her chiseled financier ex aired their dirty laundry in an eight-day custody trial with Busson accusing Thurman of mixing prescription drugs with alcohol to cope with stress. 

She fired back claiming Busson was a neglectful dad, an 'angry boyfriend' and suggested he once confided in her that he was addicted to prostitutes. 

Thurman pictured leaving  Manhattan Supreme Court following Tuesday's '98 percent' agreement

The former lovers also bickered over a $1.5 million engagement ring that Thurman allegedly refuses to return to Busson

On Monday, Justice Cooper unexpectedly declared he was hopeful of reaching a settlement, going so far as to claim the couple's differences were '98 per cent resolved'.

Talks between the sparring legal teams ran late into Wednesday night. 'This has to be for real,' Justice Cooper warned them on Thursday before inviting both teams to speak in chambers. 'If this deal happens you can sleep all weekend.' 

He emerged several hours later and told the court 'I'm delighted to say there is going to be an agreement,' adding that he was happy for Thurman, Busson but 'most of all the child'. 

French-born Busson, wearing a smart black suit and tie, spoke briefly to confirm that he understood the terms of the 38-page settlement on Thursday. 

Asked if anyone had forced him to sign, he casually said, 'yes', before correcting himself: 'no, your honor.' 

Busson's attorney Peter Bronstein asked what would happen if Thurman backed out and Justice Cooper replied: 'If Miss Thurman did not sign the agreement it would be totally null and void and I would disregard it.' But he added: 'The 0.2 percent was a little tough but I'm assured that Miss Thurman will sign.' 

Luna's court-appointed attorney, Virginia Lopreto, also signaled she was happy with the deal. 

Thurman and Busson dated for seven years and were briefly engaged until their March 2014 split, two years after the birth of their daughter, whose full name is Altalune Florence. 

The court heard she gave it back after their engagement broke off for the first time in 2008 but he presented it to her a second time after Luna was born on July 15, 2012

She has been living in New York with Thurman and her two children from actor Ethan Hawke but Busson wants her to spend more time at his homes in London and the Bahamas. 

A psychologist warned last week that the parents now have an acrimonious relationship and it was hard to question that verdict given the slew of allegations that followed. 

Busson testified last week that he sought custody of Luna because he wanted to be more involved in her upbringing and have a greater say over her school and healthcare. 

He also wants her to be raised a Catholic although Lopreto poured scorn on his claims to lead a religious way of life, pointing out he has three children outside of marriage. 

The businessman admitted in court that he once confessed to Thurman that he paid another student to take an exam at his prestigious Swiss boarding school. 

But he denied ever admitting he was addicted to prostitutes or that he was ever violent toward another former girlfriend, the supermodel Elle Macpherson, the mother of his two teenage sons. 

Busson conceded that he once offered to give up any claim toward Luna in exchange for giving up child support but said any suggestion he abandoned her was a 'complete lie'. 

The court heard he handed Luna back to her mother after a recent visit with matted hair and dirty clothes but Bronstein claimed Thurman caused a 'major drama' every time he tried to see his daughter. 

He said his client paid $30,000 for business class seats last summer when Thurman agreed to take Luna to see him in London only to find out she wanted to go because 'her lover' was in town. 

Bronstein also asked Sara Weiss, the court-appointed psychologist, to confirm Thurman was consuming a dangerous cocktail of 'serious psychiatric drugs' and alcohol but the judge cut off the questioning. 

The former lovers also bickered over a $1.5 million engagement ring that Thurman allegedly refuses to return to Busson. 

The court heard she gave it back after their engagement broke off for the first time in 2008 but he presented it to her a second time after Luna was born on July 15, 2012. 

Busson said Thurman suggested it should be put into a trust for her children but he thought it 'shocking' that Luna would only receive a third of its value.