Downing Street said: "We have got Brexit done and we can now take full advantage of the fantastic opportunities available to us".
Prime Minister Boris Johnson will shortly hold a press conference, announcing the agreement.
It comes after months of wrangling in Brussels.
In a press conference in Brussels, European Commission President Ursula von der Leyen said: "This was a long and winding road but we have got a good deal to show for it."
"It is fair, it is a balanced deal, and it is the right and responsible thing to do for both sides."
Mr Johnson tweeted a picture of himself smiling with both thumbs lifted in the air.
Success usually comes to those who are too busy to be looking for it.