- Dawson: Ruthless Ten Hag kickstarts Man United tenure
- Casemiro to Man United: Everything you need to know
- Casemiro transfer fee 2nd-biggest ever for player over 30
- Don't have ESPN? Get instant access
Varane knows all about the Brazil midfielder after their time together at the Bernabeu and said he is the perfect addition to the squad.
"I know perfectly his quality, he can bring this balance to the team and his mentality," Varane said.
"He's a warrior, so I think he will really enjoy English football. I know him.
"I think it was a perfect night for him to meet Old Trafford because the atmosphere was absolutely amazing, and he brings a victory so it's nice."
Varane and Casemiro were part of the Madrid team that won the Champions League four times between 2014 and 2018.
Varane joined United last summer in search of a new challenge, and the France international said Casemiro expressed the same reason when joining him in Manchester.
"I know exactly what he feels and why he's coming here after what he lived in Madrid," Varane added.
"He needs a new challenge, I know exactly what he feels, and I know exactly why he chose this club.
"It's a similar process that I had so obviously I wish him the best and I'm speaking with him a lot, but he didn't need me to make his choice."
He was brought back in against Liverpool to partner Lisandro Martinez at centre-back as United got their first win, and afterwards Varane was at a loss to explain why they struggled in their dismal 4-0 defeat at Brentford, only to rebound so dramatically against Jurgen Klopp's side.
"It's difficult to explain why but we didn't start the games with the same intensity, with the same fighting spirit," Varane added.
"We had the motivation but it's difficult to explain why it was starting with this low energy.
"Football it's about energy, it's about when you have to push, when you have to stay calm, when you have to attack.
"We showed great control [against Liverpool]. It was a mature performance."