With a director in place, Obama said the Consumer Financial Protection Bureau can start overseeing the mortgage companies, payday lenders, debt collectors and other financial operations often blamed for practices that helped undermine the economy.
Obama announced the move with Cordray by his side before a cheering crowd in Ohio, a politically vital state where Cordray once was attorney general.
"Every day that we waited was another day when millions of Americans are left unprotected," Obama.
Until Cordray took over, the office didn't have all the tools needed "to protect consumers against dishonest mortgage brokers or payday lenders, and debt collectors who are taking advantage of consumers," Obama said. "And that's inexcusable. It's wrong."
In political terms, the recess appointment during the congressional break raised the level of confrontation for a president seeking re-election by championing the middle class and challenging an unpopular Congress. Acting right after Tuesday's GOP presidential caucuses in Iowa, Obama sought to grab attention and show he would not be slowed, making his most brazen leap-frog over Congress.
Senate Republicans had halted Cordray's nomination because they think the consumer agency is too powerful and unaccountable.
The Senate's top Republican, Mitch McConnell of Kentucky, accused Obama of an unprecedented power grab that "arrogantly circumvented the American people."
Added House Speaker John Boehner, R-Ohio: "It's clear the president would rather trample our system of separation of powers than work with Republicans to move the country forward. This action goes beyond the president's authority, and I expect the courts will find the appointment to be illegitimate."
It was unclear who might undertake a legal fight. But people familiar with the matter said an outside private group regulated by the consumer agency might be in the best legal position.
By going around the Senate, where Democrats hold an edge but Republicans can block action, Obama essentially declared that the chamber's short off-and-on sessions are a sham intended to block him, but don't prevent him from such an appointment.
Yet it was his own party that started the practice when Republican George W. Bush was president.
In reality, Obama had little choice to get the consumer agency fully running after months of stalemate.
White House communications director Dan Pfeiffer announced Obama's move on Twitter after senior administration officials first confirmed it to The Associated Press. Obama spokesman Jay Carney said White House lawyers have determined Obama is within his bounds to appoint Cordray now.
Cordray, who's expected to take over this week, stands to serve for at least the next two years, until the end of the Senate's next session, the White House said.
At a high school in the Cleveland suburb of Shaker Heights, Obama said Republicans were only blocking Cordray because they wanted to water down consumer protections.
"I'm not going to stand by while a minority in the Senate puts party ideology ahead of the people we were elected to serve," he said.
More than a standoff over one significant appointment, the fight speaks to the heart of a presidential campaign under way. Presiding over a troubled but improving economy, Obama's must persuade a weary middle class that he is their advocate, while fending off criticism from Republicans challengers and lawmakers.
Obama has constitutional power to make appointments during a congressional recess.
Expressly to keep that from happening, Republicans in the Senate have had the Senate running in "pro forma" sessions, meaning open for business in name with no actual business planned. Democrats started the practice under Bush to halt him from making recess appointments.
The Senate held such a session on Tuesday and planned another one on Friday. Republicans contend Obama cannot make a recess appointment during such a break of less than three days, based on years of precedent, and they point to comments by Obama's own Justice Department echoing that view.
Regardless, the Obama White House now contends such an approach is a gimmick.
For all practical purposes, the Senate is in recess and Obama is free to make the appointment on his own, without Senate confirmation, administration officials said.
McConnell shot back that Obama's move "lands this appointee in uncertain legal territory, threatens the confirmation process and fundamentally endangers the Congress' role in providing a check on the excesses of the executive branch."
The president also was expected to announce other recess appointments, possibly including nominees to the National Labor Relations Board.
Republicans have had little opposition if any to the qualifications of Cordray. Their objection is with the consumer agency itself.
Obama and his team say lawmakers should try to revise the Wall Street oversight law if they don't like it, not keep the agency from performing its job.
Before his remarks Wednesday, Obama met with a family that got taken advantage of by a mortgage broker. He wanted to use their story as an example of how the consumer agency can crack down on such practices.
Obama was focusing on the most Democratic congressional district in Ohio, a Cleveland suburb, a day after Mitt Romney won Iowa's Republican presidential caucuses by just eight votes. Obama's trip signals the White House's intent to keep the president in the public eye even as the political world focuses on the GOP's selection process.