Eight years after taking the oath of office before a vast crowd at the US Capitol and 90 minutes after handing the reins of power to his successor, Barack Obama bade an emotional goodbye to Washington.

The former president arrived early Friday afternoon at Joint Base Andrews just outside Washington aboard a Marine helicopter which picked him up from the East Lawn of the Capitol following the inauguration of Donald Trump as the nation's 45th president.

In brief remarks to supporters and staff, some of whom had been with him through two terms at the White House, Obama expressed his gratitude for their efforts and invoked the themes of his presidency.

"It wasn't blind optimism that drove you to do all this work, it wasn't naivete, it wasn't willful ignorance to all the challenges that America faces," he said. "It was hope in the face of difficulty, hope in the face of uncertainty."

The crowd included several prominent former members of Obama's administration, including Chief of Staff Denis McDonough, Attorney General Loretta Lynch, Transportation Secretary Anthony Foxx, National Security Advisor Susan Rice and EPA Administrator Gina McCarthy.

The departure ceremony marked the first steps of post-White House life for Obama and former First Lady Michelle Obama.

His message of hope came an hour after his successor spoke of stopping "carnage" in America in an inaugural speech that stressed the failures of the federal government.

Obama said, "This is not a period, this is a comma." In a play on his campaign slogan, Obama continued, "Yes we did. Yes we can."

The Obamas then waved to the crowd from the top of a stairway to an awaiting airplane that will take them along with daughters Sasha and Malia, to a vacation in Palm Springs, California.

Their jet took off at 1:46pm. For the first time in eight years, their plane wasn't designated Air Force One.