The debate now moves to the Senate.
Democrats want to hold a vote before Congress adjourns at the end of the year before Republicans take a more powerful share of the Senate.
Defense Secretary Robert Gates and other senior military leaders have supported repealing the policy. A recent Pentagon study showed that most service members do not object to serving with homosexuals.
The White House, in issuing a statement in support of the repeal, stressed that the change would go into effect only after the president, the secretary of Defense and the chairman of the Joint Chiefs of Staff certify that implementation is consistent with military readiness, recruiting and retention and unit cohesion.
The House last May voted 234-194 in favor of repeal legislation as part of a larger defense bill. The measure has stalled twice in the Senate, where Republicans have objected to taking up the defense bill laded with contentious issues, including "Don't Ask Don't Tell."
A major hurdle has been a Republican pledge to block all legislation until the Senate completes work on tax cut and government funding. The Senate on Wednesday passed the compromise on extending tax cuts worked out by the White House and Republicans.
More than 13,500 service members have been dismissed under the 1993 law.
The Associated Press contributed to this report.