Telles, 27, is a full international with Brazil and an experienced player across Europe, having played in the UEFA Champions League for many years.
Over the past five seasons with FC Porto, he has scored 26 goals and registered more than 50 assists.
He has won league titles in Portugal, and also in Turkey where he played for Galatasaray.
Alex Telles said: “To join a club with the prestige of Manchester United is a huge honour. You have to work hard to get to this moment in your career and now I am coming to this club, I can promise that I will give everything in my heart to be a success here.