If confirmed by the Senate, Lew would succeed outgoing Secretary Timothy Geithner.
Lew has a long history of budget negotiations, serving as White House budget director in the administration of former President Bill Clinton and in the early years of the Obama administration.
At the White House, Obama said he hated to lose Lew as chief of staff, but, "My loss will be the nation's gain."
"Jack has the distinction of having worked -- and succeeded -- in some of the toughest jobs in Washington and the private sector," Obama said. "As a congressional staffer in the 1980s, he helped negotiate the deal between President Reagan and [former House Speaker] Tip O'Neill to save Social Security. Under President Clinton, he presided over three budget surpluses in a row. So for all the talk out there about deficit reduction, making sure our books are balanced, this is the guy who did it -- three times. He helped oversee one of our nation's finest universities and one of our largest investment banks. ...
"One reason Jack has been so effective in this town is because he is a low-key guy who prefers to surround himself with policy experts rather than television cameras," Obama said. "And over the years, he's built a reputation as a master of policy who can work with members of both parties and forge principled compromises."
Obama said Geithner, his earliest nominee, had "hit the ground running" at Treasury.
"Thanks in large part to his steady hand, our economy has been growing again for the past three years, our businesses have created nearly 6 million new jobs," Obama said.
"The money that we spent to save the financial system has largely been paid back. We've put in place rules to prevent that kind of financial meltdown from ever happening again. An auto industry was saved. We made sure taxpayers are not on the hook if the biggest firms fail again. We've taken steps to help underwater homeowners come up for air, and open new markets to sell American goods overseas.
"And we've begun to reduce our deficit through a balanced mix of spending cuts and reforms to a tax code that at the time that we both came in was too skewed in favor of the wealthy at the expense of middle-class Americans."
Geithner said Obama "made the necessary, the hard, the politically perilous choices" to fix the economic crisis.
Lew will face massive automatic spending cuts unless Congress acts by March 2 to avert the sequester and should be in the center of administration efforts to raise the U.S. debt ceiling to fund the government.
Lew has been criticized for his illegible signature, which looks like a series of curlicues. Obama said, "Jack assures me that he is going to make at least one letter legible."