The Wales international defender has signed a five-year contract with Jose Mourinho's side.
Swansea has brought in Ryan Bennett from Wolverhampton Wanderers on a three-year deal as Rodon's replacement.
Rodon, who had previously been linked with West Ham United, has played 52 Championship games for Swansea since breaking into the first team during the 2018-2019 season.
He is Mourinho's eighth signing of a busy transfer window for Spurs, which faces West Ham in the Premier League on Monday (AEDT).
As well as making Giovani Lo Celso's move from Real Betis permanent, Spurs have also signed Sergio Reguilon, Matt Doherty, Pierre-Emile Hojbjerg, Carlos Vinicius, Joe Hart and Gareth Bale.
Rodon's signing takes their reported transfer spend to a little less than £100 million ($181.7 million), less than seven months on from their initial decision to impose a 20 per cent pay cut on 550 staff members because of the financial impact of the coronavirus pandemic.
After criticism, Spurs announced in April that all staff members, including those placed on furlough, would receive 100 per cent of their pay for April and May and that the board would instead take salary reductions.
Meanwhile, Spurs defender Cameron Carter-Vickers has moved to Bournemouth on loan for the rest of the 2020-2021 season.