The decisions are to mark the "exceptional circumstances" of the
It means Wembley will host an unprecedented two finals in the space of three years after the success of the Barcelona-Manchester United final last month. The decisions were passed unanimously by UEFA's executive committee meeting in Nyon, Switzerland.
It will be the seventh time that Wembley has hosted the Champions League or European Cup final, the most of any venue. The stadium hosted the final previously in 1963, 1968, 1971, 1978, 1992 and most recently last month.
Platini said: "There are always many candidates for the Champions League final and the Congress but this is to mark the special year of the English FA."
The UEFA Congress will be held in London in the days leading up to the final. FA chairman David Bernstein said: "We are delighted Wembley Stadium has been chosen to host the 2013 Champions League final.
"UEFA viewed the 2011 Champions League Final at Wembley as a major success and today they have paid us the ultimate compliment by announcing that they will return to our national stadium in 2013, the year of the FA's 150th anniversary.
"It will be a major celebration of football in this country during a landmark year for our organisation and is an acknowledgement of Wembley's status as one of the very best football stadiums in the world."
Wembley Stadium chairman Melvin Benn added: "It was always our aim to deliver the best ever Champions League final in May to maximise our chances of getting it back.
"The fact that this announcement has come so soon after the success of the 2011 final shows just how impressed UEFA was with our stadium and with our team. Wembley is a world-class stadium and was built to stage the very biggest and best events.
"I would like to thank managing director Roger Maslin and the whole team at Wembley for delivering such a fantastic final in May. We will now look forward to working with UEFA and putting on a spectacular final in 2013."
UEFA aware of 'historic moment'
Platini added: "Founded in 1863 the Football Association is the oldest of all the national football associations and in 2013 it will celebrate its 150th anniversary.
"Given the exceptional nature of this historic moment in our beautiful game, and the fact that we will also celebrate 150 years of the Laws of the Game, we felt it was our duty at UEFA to help the FA celebrate in some special way.