Gil enjoyed an impressive loan spell at Eibar last season and is on international duty with Spain at the Tokyo Olympics.
The 20-year-old has also enjoyed success in his short career, helping the Spain Under-19 side win the 2019 European Championship.
Coming 🔜 pic.twitter.com/SvWX95uRby— Tottenham Hotspur (@SpursOfficial) July 26, 2021
Gil's arrival means that Lamela ends his eight-year spell at the Premier League club after making 257 appearances and scoring 37 goals.
Foillowing the announcement of the deal, Spurs tweeted: "A player who gave everything for the badge. Thank you, @ErikLamela."