Casemiro was introduced as a Manchester United player before the club's home game with rivals Liverpool on Monday after joining from Real Madrid.
United will pay up to £70m for the Brazil midfielder, who has signed a four-year deal at Old Trafford.
Casemiro says he is joining "the biggest team in the world" after bidding an emotional farewell to Real.
The 30-year-old becomes one of the top earners at Old Trafford but he says the move is not motivated by money.
After joining from Sao Paulo in 2013, Casemiro helped Real win the Champions League five times, plus La Liga three times and the Cope del Rey once.
He started last season's Champions League final, as Real beat Liverpool to become European champions for the 14th time, and he made his 336th appearance for the Spanish giants as a substitute in last week's opening-day win at Almeria.
He bid an emotional farewell to the Spanish champions on Monday, before travelling to Manchester.
