Christian MP Fiona Bruce tabled the motion in the House of Commons, which also calls on the United Nations Security Council to bring members of IS to justice for their crimes, which include mass killings and sexual slavery.
Similar motions were passed earlier this year with support from MEPs at the European Parliament, US Congress and also US Secretary of State John Kerry.
278 MPs voted in favour with 0 against.
Speaking during the debate, Fiona Bruce said: "Genocide is a word of such gravity, implications and history, that it should never be used too readily. It is rightly known as the "crime above all crimes". For this reason alone it is incumbent upon all of us to prevent the term from devaluation or over-use.
"But such caution must not stop us from naming a genocide where one is taking place.
"The proposers of this motion are here to insist that the overwhelming evidence of the atrocities of Daesh in Syria and Iraq is recognised for the genocide it is, and is considered as such by the UN Security Council and International Criminal Court - and to support similar resolutions of other leading international and legislative bodies.
"There are only two possibilities here. If the House is not satisfied that genocidal atrocities are being perpetrated, we must not pass this motion, on which I am minded, Mr. Speaker, to test the will of the House. But if colleagues believe that the depravities of the Islamic State, or ISIS or IS or, as we now refer to is in this place, Daesh, are being undertaken with genocidal intent, then we have already waited too long to recognise these atrocities as what they are a genocide."
Foreign Office minister Tobias Ellwood told MPs that he believed Genocide has taken place but that it was a matter of legal opinion.
The UK Government, unless it refuses Parliament's decision, must now draft a motion to go before the UN Security Council, to the effect that the International Criminal Court can begin proceedings against Daesh fighters accused of committing genocidal acts. The motion should then be voted on by the UN Security Council, requiring a unanimous vote.
Listen to Fiona Bruce speaking before the vote on Premier's Inspirational breakfast: