United made Maguire the most expensive defender in world football when they signed him for a reported 80 million pounds ($96.40 million) from Leicester City in the close season.
The fee eclipsed the previous record of 75 million pounds that Liverpool paid Southampton for Van Dijk in early 2018.
Maguire must live with the price tag pressure: Van Dijk
Evans, who came through the United youth system and spent more than a decade at Old Trafford, backed Maguire to quickly become a fan favourite with his new club.
"I don't have any worries about him there," the Leicester defender told British media.
"He's tailor-made for Manchester United, it was a great move for him. He's a player they needed... He will be a real hit there."
Van Dijk has been a transformative presence for Liverpool since joining the Merseyside club, helping them win the Champions League last season and take the Premier League title race down to the wire.
Maguire gives Man Utd plenty of cause for optimism after 4-0 win over Chelsea
Maguire, 26, made his United debut in Sunday's 4-0 Premier League victory over Chelsea and showed signs of similar promise with a performance that earned him the man-of-the-match award.
"Both are great on the ball and Harry has got explosive pace people don't see," Evans added. "He is powerful and good in the air.
"Everyone will compare the transfer fees but it's so difficult to judge transfer fees nowadays. We're all human and it is weird we get traded for money.
"In the transfer market it's all supply and demand and things can go up and down at any moment. The most important thing is for him to be judged on how he plays."
United's next assignment is a league trip to Wolverhampton Wanderers on Monday.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ