United signed left-back Reguilón on a season-long loan deal from Tottenham while Evans has put pen to paper on a one-year deal at Old Trafford.
"In life you have to be ready for everything and the chance to represent this great club with such an illustrious history is one that I could not turn down," Reguilón said in a statement.
"Having spoken to the manager, I know what he needs from me, and I am ready to play my part in helping the team to achieve success," he added.
"I know that I can contribute to Manchester United this season; I am ready to fight for this group and show everyone my qualities."
United's transfer activity is not done yet, either, with the club working on a deal to bring in Fiorentina midfielder Sofyan Amrabat on loan with an obligation to make it a permanent deal, sources have told ESPN.
Sources have told ESPN that United were only able to make a move for Amrabat, 27, after agreeing Dean Henderson's move to Crystal Palace. Henderson joined Palace on Thursday in a deal which could rise to £20 million ($25.4m).
Evans, who left Leicester City at the end of last season, initially signed a short-term contract to cover this summer's preseason games but will stay at United for another year.
"I am delighted to join Manchester United, a place which has always felt like home" Evans said. "This club and the fans have shaped me as a player and as a person since I was 15 years-old, and I am delighted to be back where it all began as part of this talented squad.
"I've really enjoyed working under the manager and his coaching staff since the start of pre-season, and I'm looking forward to helping this group achieve success together at this fantastic football club."