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.
The planned lawsuit is expected to generate 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, a Democrat, exceeded his executive authority in making unilateral changes to the Affordable Care Act, known as Obamacare.
Republicans argue that by delaying some healthcare coverage mandates and granting various waivers, he bypassed Congress in violation of the US Constitution.
Republicans have complained about other unilateral actions that Obama has taken to advance his agenda, from executive orders on immigration policy to same-sex partner benefits.
But they have narrowly focused the suit on the healthcare law because "it is the option most likely to clear the legal hurdles necessary to succeed," said Republican Representative Pete Sessions of Texas, who chairs the House Rules Committee.
"This administration has effectively rewritten the law without following the constitutional process," Sessions added.
Democrats have slammed the lawsuit effort as a politically motivated waste of taxpayer resources while Congress has failed to act on other pressing issues including emergency funding to deal with a flood of migrant children.
"This is a veiled attempt at impeaching the president," said Democratic Representative Sheila Jackson-Lee of Texas. REUTERS