The 225-201 vote along party lines means House lawyers will now draft legal documents to launch a lawsuit.
Its supporters say Mr Obama exceeded his powers when he delayed an insurance deadline in his healthcare law.
The president himself has dismissed it as a waste of time. “Everyone sees this as a political stunt,” he said.
“If they’re not going to do anything, we’ll do what we can on our own,” the president added.
“And we’ve taken more than 40 actions aimed at helping hardworking families like yours. That’s when we act – when your Congress won’t.”
The action is reportedly the first time either the House or Senate has brought legal action against a president over the legality of his powers, although members of Congress have sued the president before.
Republicans in Congress have complained that Mr Obama has exceeded his constitutional authority on numerous occasions, in order to bypass Congress by issuing executive orders.
They object, for instance, to his order unilaterally easing deportations of some young illegal immigrants, and the prison exchange that won the release of a US soldier held captive for five years by the Taliban.
“This isn’t about Republicans or Democrats. It’s about defending the Constitution we swore an oath to,” Speaker John Boehner said during an impassioned debate in the House on Wednesday evening.
“Are you willing to let any president choose what laws to execute and what laws to change?”
At issue was Mr Obama’s decision to twice delay requirements in his 2010 healthcare overhaul that businesses over a certain size provide their workers with health insurance.
Mr Obama has been forthright about his intentions to circumvent the gridlocked Congress when possible, noting frequently that the Republican-controlled House of Representatives has declined even to hold votes on Senate-passed bills on topics from immigration reform to gay rights.
As far back as January, White House aides began referring to the president’s “pen and phone” strategy – using his telephone to convene meetings at the White House and his pen to sign executive orders and changes to federal regulations.
Every US president since George Washington has issued executive orders, and Mr Obama has not stood out in the modern era for the number he has signed.
In his six years in office Mr Obama has issued 183 executive orders, compared to 291 across George W Bush’s eight years and 381 for Ronald Reagan, according to a study by the American Presidency Project at the University of California-Santa Barbara.
But Republicans insist Mr Obama has selectively enforced laws duly passed by Congress, upsetting the balance of powers written into the constitution.
“Such a shift in power should alarm members of both political parties because it threatens the very institution of the Congress,” the Republicans wrote in report accompanying the House legislation.