United paid an initial £34m for World Cup winner Varane in August 2021, and he received a memorable reception before their opening Premier League game of last season
The France international, 29, joined United last summer, but a combination of injuries and his new team's form cast a shadow over his debut season.
By leaving Real Madrid, he missed the chance to win a fourth La Liga title, and a fifth Champions League success.
But he rejects the notion he made the wrong choice, telling BBC Sport: "No, absolutely not."
He added: "In football, you have to challenge yourself and try to improve. I wanted to live another experience after 10 years in the same place.
"The Premier League is absolutely fantastic and Manchester United are a great club. There was no doubt about my decision."
As Varane is aware, there is a difference between challenging yourself and challenging for major honours - as he did from the moment he joined Real in 2011.
Given the gulf between United, and Manchester City and Liverpool - who both finished more than 30 points ahead of the Red Devils last season - the latter seems a long way off.
However, with new manager Erik ten Hag trying to bring greater speed and fluency to United this season, Varane can see reason for optimism.
"It's a new season. A new start," said Varane.
"Confidence is important and we lost confidence when we lost some games. But I think we have great potential.
"The new manager is very positive. He wants this energy and to press high up the pitch, with more space behind our backs. That is maybe more offensive but it is football we really enjoy, so that is a good start."
One of Ten Hag's most significant moves this summer has been to pursue Argentina international Lisandro Martinez, who played for him at Ajax.
Martinez's arrival is yet to be confirmed, but it is anticipated he will be involved on 30 July, when United head to Oslo to face Atletico Madrid.
Ten Hag has spoken about Martinez's qualities as a left-sided player, and switched captain Harry Maguire to the right in Tuesday's encounter with Crystal Palace in Melbourne.
Given the United manager has confirmed Maguire will continue as captain this season, it would seem to place Varane's position in the team in doubt.
Not that the player views the situation in quite the same way.
"Competition is good for the team," he said. "Harry is a very important player for us. He's the captain and obviously he has a lot of good qualities.
"The team will always be better with this competition. Every great club is like this. If everyone wants to fight for the team, that's a good thing."
Varane spent seven years as Cristiano Ronaldo's team-mate at Real Madrid, before being reunited with the Portuguese at United.
The 37-year-old's future is still to be clarified amid an ongoing absence from pre-season training because of a family matter and his desire to play for a club capable of competing for the Champions League.
For those who argued Ronaldo's inability to press was a major reason for United's troubles last season, it would be a benefit if he moved. For those who felt he was the only reason the club did not completely fall apart, it would be a major blow.
"That debate was outside of the dressing room," said Varane.
"We know his quality. And we know he's very famous. So we know a lot of people will speak about the performance of the team and his performance.
"Cristiano is a great competitor. He's a legend and he always helps the team, so obviously it's very good to play with him."
-- Courtesy of BBC Sport