The 26-year-old striker left for the Spanish capital on loan back in January going on to score seven goals in 17 appearances for the Rojiblancos.
And it was announced by both clubs on Saturday that the switch will become a permanent one following the initial loan which ends at the end of the 2019/20 season.
"We would like to thank Alvaro for his contribution and wish him the best of luck for the future," Chelsea said in a statement on their official website.
Morata scored 24 goals in 72 appearances for the Blues after joining from Real Madrid in 2017 in a then club record £57m move.
But with new boss Frank Lampard assessing his squad following his appointment as manager earlier this week it is clear he is not in his plans.
Morata's exit follows the club's decision not to keep Gonzalo Higuain for a second season on loan leaving Olivier Giroud, Michy Batshuayi and Tammy Abraham as the Blues' only senior strikers in the first team squad.
The Spaniard joins Joao Felix, Hector Herrera and Marcos Llorente as new arrivals at the Wanda Metropolitano this summer.
Morata's stay should accelerate Antoine Griezmann's departure with the French international widely expected to move to Barcelona imminently despite a very public fallout between the two clubs.
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