The 225-201 vote, along party lines, to authorize the suit will allow House lawyers to draft legal documents over a five-week summer recess starting on Friday.
It cements the action as a lightning rod for months of bitter campaign rhetoric from both Republicans and Democrats ahead of November elections that will determine the political control of Congress next year.
The suit is expected to claim that Obama exceeded his executive authority in making unilateral changes to the Affordable Care Act, known as Obamacare.
"The lawsuit has intellectual merit because we want to show that we're not going to take this lying down," House Budget Committee Chairman Paul Ryan said at a breakfast hosted by the Christian Science Monitor. "The president is issuing executive orders and regulations that exceed the parameters of the statutes that give him the authorities in the first place."
With Republicans in control of the House, Obama's agenda has been thwarted by congressional gridlock, leaving him to take executive actions to make changes where he has the power to do so.
The president has been delivering variations of a fiery stump speech all summer as he tours the country trying to motivate Democrats - and wealthy donors - to get involved in November's congressional elections.
His aim is to energize Democratic voters ahead of the elections in hopes of stopping Republicans from gaining control of the Senate, which, if joined with a Republican hold on the House, could make it extremely difficult for him to pursue his agenda in his last two years in office.
Polls show Democrats will have a hard time holding control of the Senate in the midterm elections, while Republicans are expected to keep control of the House.
Republicans have criticized Obama for his road trips, saying his time would be better spent addressing a series of domestic and foreign crises.