Mbappe, 25, will move to the Bernabeu Stadium on a five-year deal when his Paris St-Germain contract expires on 30 June.
He will earn 15m euros (£12.8m) a season, plus a 150m euro (£128m) signing-on bonus to be paid over five years, and he will keep a percentage of his image rights.
“Nobody can understand how excited I am right now!” Mbappe posted on Instagram.
“A dream come true. So happy and proud to join the club of my dreams.”
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He will join a Madrid side fresh from winning La Liga as they captured a record-extending 15th European crown with victory over Borussia Dortmund in the Champions League final.
Mbappe’s arrival in the Spanish capital is likely to prompt suggestions of a new Galacticos era at the club given the exciting prospect of him lining up alongside Brazil forwards Vinicius Jr, Rodrygo and fellow new signing Endrick, and England midfielder Jude Bellingham.
Mbappe verbally agreed to join Real in February and announced in May he would leave the French champions at the end of the season.
He leaves the French capital as PSG’s record goalscorer, with 256 goals since he joined from Monaco on an initial loan in 2017.
The forward scored 44 goals in 48 matches last term and has been the leading scorer in the French top flight for the past six years.
At club level, he has won seven Ligue 1 titles – the first of those with Monaco, the remaining six with PSG – and has collected four winners medals in the French Cup.
The Frenchman won the Golden Boot at the 2022 World Cup in Qatar, where France lost to Argentina on penalties in a dramatic final.
However, he is yet to triumph in the Champions League, having been a beaten finalist in 2019-20 – something he will hope to rectify with a club that has made a habit of winning Europe’s elite club competition.
