Mr Tusk, the president of the European Council, announced the news on Twitter.
The 27 leaders gave it their backing after less than an hour's discussion in Brussels.
Todays decision includes the political declaration, which sets out what the UK and EU's relationship may be like after Brexit and the EU withdrawal agreement, which is a 585-pages long and legally binding document setting out the terms of the UK's exit from the EU.
The UK Parliament is expected to vote on the deal in early December but its approval is by no means guaranteed,
Prime Minister Theresa May has appealed to the public to support the agreement, arguing it is the best deal she could have struck
EU-commission president Juncker commented on the deal before todays meeting that it's the best deal possible and the European Union will not change its fundamental position when it comes to this issue.
He further stated that he thinks that the British Parliament, because this is a wise parliament, will ratify the deal.
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