In a tight vote, several Republicans previously opposed to aspects of the plan changed their minds.
Prior attempts to replace Obamacare have collapsed in recent weeks due to divisions in the Republican party.
President Trump had made scrapping the policy a key campaign pledge.
Before the vote took place, Mr Trump had warned his party's senators of the repercussions of not pushing through the measures to repeal and replace Obamacare, known formally as the Affordable Care Act.
