The 19-year-old, who has made seven first-team appearances, has signed a five-year contract after the Red Devils agreed to pay Porto £19m for him.
Dalot has represented Portugal from under-15 to under-21 level and made his Porto debut in October.
“The chance of coming to the biggest club in the world is something I just couldn’t turn down,” said Dalot.
Dalot came through the youth ranks at Porto and played in a 0-0 draw against Liverpool in the Champions League last 16 in March.
He is expected to provide competition for United captain Antonio Valencia.
“In his age group, he is the best full-back in Europe,” said Mourinho.
“He is an extremely talented young defender with all the qualities to quickly become a great player for this club.
“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.”
The transfer should hasten the exits of Italian full-back Matteo Darmian, who has been strongly linked with Juventus, and Netherlands defender Daley Blind. Neither player has a long-term future under Mourinho.
He is determined to strengthen his defence for what he hopes will be a far closer Premier League battle with champions Manchester City next term.
United announced on Tuesday that they have agreed a deal for Shakhtar Donetsk’s Brazil midfielder Fred, for a reported £47m.