Cucurella joins Chelsea in a deal worth an initial £56m with a possible £7m in add-ons. Chelsea's Levi Colwill will join Brighton on a season-long loan in return for the Cucurella transfer. The loan deal does not include an option to make the transfer permanent.
In a press conference on Friday, Thomas Tuchel said: "Marc is a fantastic player, a young player. He is young, hungry, mobile and a very intelligent player who can play a lot of positions in our system."
On signing for Chelsea, Cucurella said: "I'm really happy. It's a big opportunity for me to join one of the best clubs in the world and I'm going to work hard to be happy here and help the team."
Cucurella, 24, was wanted by Manchester City and Cucurella handed in a transfer request but the two clubs couldn't strike a deal, with Brighton standing firm on a £50m valuation for the left-back. The deal stalled, as sources told ESPN that City weren't willing to pay the asking price for the transfer, allowing Chelsea to battle for his signature.
Sources told ESPN that City were only interested in signing the Spain left-back if the asking transfer fee was lowered to £35m.
Chelsea chairman Todd Boehly said: "Marc is an elite defender of proven Premier League quality and he further strengthens our squad going into the new season. We continue to work on and off the pitch, and we're delighted Marc will be a part of the present and future at Chelsea."
Throughout the transfer window, Tuchel has looked to bolster his defensive options with Antonio Rudiger and Andreas Christensen joining Real Madrid and Barcelona respectively. Chelsea wanted to sign Matthijs de Ligt and Jules Kounde, but the two defenders opted to move to Bayern Munich and Barcelona.
Cucurella, who won Brighton's player of the season award last season, played 38 games during his one year stay with Graham Potter's team.