"I'm confident she will serve with distinction on the federal bench," Obama said.
In Tuesday's vote, Sens. Susan Collins of Maine and Lisa Murkowski of Alaska were the only Republicans to join Democrats in supporting Millett.
The Senate then approved a series procedural votes setting up a final vote on Rep. Mel Watt, D-N.C., to head the Federal Housing Finance Agency. Democrats again took advantage of the weakened filibuster rules, voting 57-40 to move forward Obama's pick to head the agency that oversees mammoth home mortgage lenders Fannie Mae and Freddie Mac, which own or guarantee about half of all U.S. mortgages. Two Republicans, Richard Burr, of North Carolina, and Rob Portman, of Ohio, voted with Democrats.
Republicans say Watt is unqualified to lead the agency. Democrats say Watt, a 21-year House veteran, has the necessary skills and is opposed by Republicans because they think he is too liberal.
Millett, the first nominee to emerge from the highly partisan filibuster fight, is a veteran attorney who has argued 32 cases at the Supreme Court and has strong bipartisan credentials.
A Harvard Law School graduate, Millett served as an assistant to the solicitor general under President Bill Clinton, a Democrat, and President George W. Bush, a Republican. She then joined the Supreme Court practice at Akin Gump, one of Washington's biggest law firms.
Over the next two weeks, Democratic leaders also plan to win final Senate approval for two other Obama nominees to the D.C. Circuit, as well as his picks to head the Federal Reserve and the Department of Homeland Security.
Tuesday's votes came the morning after Republicans responded to changes Democrats made to Senate filibuster traditions by slowing down 76 mostly minor nominations.
The move by Senate Republicans won't stop any of the nominations — Democrats can now approve them by a simple majority. But it showed Republicans would make Democrats pay a price for their decision to change filibuster practices and showed that tensions over nominations are still roiling the Senate.
Last month, Democrats used their effective 55-45 majority to upend decades of Senate filibuster traditions and allow simple majority votes on most presidential appointments, excluding Supreme Court nominees. Before the change, the president's party needed 60 votes to prevent opposing senators from blocking a nominee.
Republicans continued to assail Democrats for the maneuver Tuesday. Republican Leader Mitch McConnell said that "for the president and his enablers the ends now clearly justify the means."
Sen. John McCain, R-Ariz., promised to support tactics to delay nominees saying he hadn't gotten a chance to properly scrutinize nominees, including Jeh Johnson, Obama's pick to lead the Department of Homeland Security.
"It'd be fine with me," McCain said, when asked if that meant long nights or sessions bumping up against the holiday break.
McCain's comments came after Senate Majority Leader Harry Reid on Monday asked for unanimous approval of 76 nominations — including Johnson and Janet Yellen to lead the Federal Reserve. Sen. Lamar Alexander, R-Tenn. rose to object slowing but not stopping the nominations.