If confirmed by the US Senate, Yellen would replace Ben Bernanke, who has held the post for eight years, the BBC reports.
She has been his deputy for the last two years, and would become the first woman to head the Federal Reserve.
Yellen and Bernanke are due to appear with the president on Wednesday.
She has taught at Harvard University and the London School of Economics, as well as holding a series of senior administrative positions in the US.
Yellen, like Mr Bernanke, is seen as a “dove”, meaning she prefers to prioritise boosting employment by keeping rates low rather than worrying about inflation.
Her nomination has been widely expected after former Treasury Secretary Larry Summers withdrew his candidature.
One senior US senator, Democrat Charles Schumer, said Yellen had the backing of politicians and would win Senate confirmation “by a wide margin”.
The chairman of the US Senate Banking Committee, Tim Johnson, said she had “a depth of experience that is second to none”.
“I have no doubt she will be an excellent Federal Reserve chairman,” he added.