Dalot, 19, has signed "a five-year contract, with an option to extend for a further year", United said in a statement.
Brazilian international midfielder Fred joined United from Shakhtar Donetsk for a reported fee of just over £50 million on Tuesday.
United are aiming to close the gap on Manchester City, who won the Premier League by a record 19 points from their local rivals.
Despite only making his senior Porto debut in February, Dalot has been hailed by United manager Jose Mourinho, who made his name as a coach with Porto, as the best full-back in Europe of his age.
"Diogo is an extremely talented young defender with all the qualities to quickly become a great player for this club," Mourinho said in United's statement.
"He has all the attributes that a full-back needs: physicality, tactical intelligence and technical quality, combined with a Porto Academy mentality which prepares players for the maturity they need at the professional level.
"In his age group, he is the best full-back in Europe and we all believe he has a bright future ahead of him at Manchester United."
Dalot's best position is at right-back, although he has at times deputised at left-back, including in a 0-0 draw away to Liverpool in the second leg of the Portuguese champions' Champions League last 16 tie in March.
Full-back has been a problem position for United with Mourinho using converted wingers Ashley Young and Antonio Valencia, both 32, as regulars in his defence over the past year.