The vote on Yellen's nomination was seen as a crucial test of President Barack Obama's most important second-term nominations, CBS News said.
The term of current Federal Reserve Chairman Ben Bernanke expires at the end of January.
Senators voted 59-34 to end debate on her nomination. A final confirmation vote will take place Jan. 6, when the Senate returns from its holiday recess.
The senators had been gearing up for a rare weekend session as Republicans and Democrats were at odds about when to hold votes on the handful of nominations remaining on the Senate's docket.
During their closed-door caucus Thursday, Senate Democrats were told they would be staying in Washington through Saturday, while Senate Republicans came up with a plan to have one of its members on the floor while Democrats met, Politico said.
Three other Obama appointees were confirmed by the Senate Friday, including John Koskinen as Internal Revenue Service commissioner, Alejandro Mayorkas as Department of Homeland Security deputy secretary and Brian Davis as federal judge in Tampa, Fla.