Everton were also interested in the Spaniard but the 2010 World Cup winner has decided to move to Spurs after agreeing a two-year deal, with the option of a further season.
The Blues tried to sign Llorente during the January transfer window and stepped up the negotiations with Swansea earlier this week.
On Tuesday (29 August) Chelsea looked very close to striking a deal with Swansea, subject to the south Wales club finding a replacement before the end of the transfer window.
However, 24 hours the deal came under scrutiny after Tottenham launched a last-ditch attempt to hijack Chelsea's pursuit and lure the Spaniard to White Hart Lane.
Mauricio Pochettino's side had the bid accepted by Swansea on Thursday morning [31 August] after agreeing to improve the terms previously offered by the Blues.
Chelsea tried to react and quickly match the offer with the hope he could be tempted to reunite with his former Juventus manager Antonio Conte at Stamford Bridge.
However, the 32-year-old striker has decided instead to join Tottenham in a two-year deal, with the option of a further season.
Llorente becomes Tottenham's fifth signing of the summer following the previous arrivals of right-back Serge Aurier, defender Juan Foyth, goalkeeper Paulo Gazzaniga and centre-back Davinson Sanchez.
The towering striker only joined Swansea from Sevilla last summer after having previously garnered a big reputation during his spells at Juventus and Athletic Club Bilbao.
The former Spanish international enjoyed an impressive debut in the English football, playing a key role in avoiding Swansea's relegation by scoring 15 goals in 33 Premier League appearances. The Wales side blocked his departure during the January transfer window when Chelsea tried to sign him to serve as a back-up for Diego Costa during the second part of the 2016-2017 season.
But Paul Clement's side have given the green light to the deal after the club secured the return of Wilfried Bony from Manchester City as his replacement.
LLorente scored 18 goals under Conte at Juventus in the 2013-2014 campaign after the Italian boss recruited him from Athletic Club during the summer of 2013. The Chelsea manager believed that the veteran striker would compliment fellow new addition Alvaro Morata in his attack, with the two Spanish pair having a strong relationship after playing together in Italy.
However, the towering striker will instead play in the other part of London and will serve as a back-up for Harry Kane.