It has to go to the House of Lords next for them to pass it, or as usual with these sorts of things it will get passed back to the Commons for them to make changes before it goes back again. It's basically a game of Pong across Westminster, before they both agree and then it will go ahead.
How it goes in The Lords is anyone's guess as the people in the Lords are quite a mixed bunch or Pro and Anti Europe. I'm personally hoping (aside from the whole thing being kiaboshed) for the Lords to pass it back asking for a change to the bill to put the terms of the deal back to the public vote, which is what the Lib Dems are asking for.
Whilst a great deal of MP's are pro European, they're having to do that whole "well my constituency voted for it, so I'll have to"... even though they don't want to, but politics gonna politics. But they may try and at least make the deal the best they can to avoid the Brexit deal being bad (a Hard Brexit) and not in the National Interest. However, because politics gonna politics, they (mainly the Tories) will unfairly be "threatened" by the party whips to, in the words of that f*cknugget of s spokesman for Mr Orange, Sean Spicer... "get with the programme", and have to do what the leaders are trying to do (which is a hard Brexit and is a bad idea). Where as if they can get the amendment in to put it back to the public, it helps to swing it back towards a soft Brexit, as there is still an air of "voters remorse" within the UK, so this may help soften the blow. And hopefully leave the door open for a future re-entry, once the sh*t has really hit that fan and people realise what they've done, and want back in.
There is a valid argument and it's very valid indeed, that whilst the "majority" of people voted for Brexit, the vote did not specify the terms of the exit, should it be voted in favour. So setting out the terms for the deal and putting back to the public will ensure that that the people, who this will affect the most, are fully informed and are the ones to vote of the deal in an impartial vote, as opposed to some sort of forced vote by MP's and their party leaders.