The 25-year-old captain of the French national team had revealed he was leaving Paris St Germain in a video posted on social media platform X, formerly twitter, on May 10.
Mbappe will complete the move in July after his PSG contract expires on June 30, but will be unveiled before joining up with the France squad for the European Championship in Germany.
Mbappe joins a star-studded side in Madrid with the likes of Ballon d'Or favourites Vinicius Jr. and Jude Bellingham, led by Italian Carlo Ancelotti -- the most successful coach in Champions League history with five titles.
Although Mbappe won several trophies at PSG, often completing domestic doubles and trebles, the Champions League has eluded him and remains the only major honour left to complete his sparkling resume.
Mbappe leaves PSG after seven years at the club in which he won six Ligue 1 titles and four French Cups, finishing his career in the capital city as the club's all-time top scorer with 256 goals.
The 2018 World Cup winner surprised PSG last year when he sent a letter stating he would not take up the option of a one-year contract extension.
The letter led to a stand-off with the club and Mbappe was omitted from the first-team squad before being re-instated.
Mbappe running down the final year of his contract meant PSG were unable to recoup any of the 180 million euro ($A290m) transfer fee they paid in 2017 to sign him from AS Monaco.
Real Madrid courted Mbappe in the past but failed to land the player, who signed a contract extension with PSG in May 2022 when the Spanish club had a bid rejected.
With Mbappe finally in their ranks, the club can look at consolidating their dominance in LaLiga where they lost only once last season to win the title by 10 points. They were also unbeaten as they won the Champions League for the 15th time.
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