Of course, all of the celebrations are undoubtedly premature as the bill will now be sent to the Senate where it will likely have to be substantially modified in order to attract 51 Republican votes.  Per the Washington Post, here is what happens next:

Bill must pass Senate

Because Republicans hope to pass this legislation under the less-onerous budget
reconciliation process, which would allow it to pass the Senate with only 51 votes, House leaders must make the bill comply with the Senate's "Byrd Rule." Generally, the rule says a reconciliation bill must relate to the budget, which means some of the Affordable Care Act's provisions cannot be addressed via this process because they do not deal with taxes or spending. It also stipulates that the law cannot add to the deficit in the long term (10 years after it is implemented).

It will be up to the Senate parliamentarian to decide whether the legislation meets the Byrd Rule standards. Democrats have said that the bill does not meet the standard, something Republicans sacrificed in favor of a more complete repeal.