The nomination follows months of political infighting over the choice of her versus former Treasury Secretary Larry Summers.
Yellen's nomination is already encountering stiff opposition. On Tuesday the Senate's number two Republican, John Cornyn, expressed concerns about her.
Obama spent much of his address celebrating Bernanke's work as chairman.
"He has truly been a stabilizing force, not just for our country but for the entire world," the president said.
Following Obama's remarks, Yellen said she was "honored and humbled" by the nomination.
"The past six years have been tumultuous for the economy and challenging for many Americans," she said, adding "We have made progress. The economy is stronger and the financial system sounder."