The transfer also sees Erik Lamela leave the north London club to join Sevilla on a three-year deal.
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.
Gil’s arrival means that Lamela has ended 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.”