The Spain left-back enjoyed an outstanding single season at Brighton, having joined from Getafe last August.
With City selling Oleksandr Zinchenko to Arsenal, it appeared Cucurella was set to sign for the Premier League champion.
However, it was widely reported Brighton was standing firm with its demands of that fee while City was only willing to pay £40 million ($69.8 million).
Brighton head coach Graham Potter last week described the club as "confident and relaxed in our position" as it awaited a further bid from City.
Instead, it came from Chelsea, with the Blues moving quickly to sign Cucurella on a six-year deal. He follows Raheem Sterling and Kalidou Koulibaly in signing for the London club ahead of the new season.
His arrival comes as a big boost to Thomas Tuchel, who has seen top targets Matthijs de Ligt, Jules Kounde and Raphinha go elsewhere.
With Marcos Alonso – another Spain international – linked with a move to Barcelona, ex-Blaugrana academy graduate Cucurella appears set for a battle with Ben Chilwell for a starting spot, although it has been suggested the new recruit could play in a back three.
Injury restricted Chilwell to seven appearances in the Premier League last season, although he still scored three goals and provided an assist. Cucurella, in 35 matches, netted just once and could also only match Chilwell's single assist.
But Cucurella also showed why he would be a good fit for any team competing at the top end of the table.
The 24-year-old enjoyed 2,827 touches, ranking seventh among Premier League defenders; each of the six players above him played for either City (Joao Cancelo, Aymeric Laporte), Liverpool (Trent Alexander-Arnold, Virgil van Dijk) or Chelsea (Thiago Silva, Antonio Rudiger).
Despite his sole assist, Cucurella finished sixth among defenders for chances created, with his 42 just behind Blues duo Reece James (48) and Alonso (43).
Cucurella ranked sixth among defenders for duels contested (323), winning a solid 59.1 per cent.
Listed at 1.72m tall, Cucurella is shorter than Lisandro Martinez (1.75m), the Premier League's smallest nominal centre-back, but he still won 52.6 per cent of his aerial duels last term, bettering the 44.7 per cent of James – another Chelsea star who switched between wing-back and centre-back roles.