The 2010 World Cup winner was poised to move to Stamford Bridge during the summer after the Premier League champions initially tried to sign him from Swansea City during the January transfer window.
Antonio Conte previously coached Llorente at Juventus and earmarked his signing as a Chelsea priority after the Spaniard enjoyed an impressive debut campaign in the Premier League with Swansea, scoring 15 goals in 33 appearances to help the Welsh side avoid the relegation.
Llorente, 32, also played alongside Alvaro Morata at Juventus and Conte wanted to reunite the two Spaniards at Chelsea to fill the big gap left by Diego Costa, who remains exiled from the first-team.
However, only 24 before the transfer deadline it emerged that Pochettino had launched a last-ditch attempt to hijack Chelsea's pursuit and lure the Spaniard to North London.
"I'm very happy because at the end everything came out perfect. Tottenham are an amazing club with a wonderful project and I think I fit in very well. I want to put my contribution on it and hopefully I can score many goals to help the club to achieve their targets," Llorente explained to reporters after making a late cameo debut in Tottenham's 3-1 victory over Borussia Dortmund on Wednesday night (13 September).
"It is clear that Pochettino played a very important role in the decision. I have known him since he was playing in Spain. There is even a nice anecdote because I made my first-team debut (with Athletic Club Bilbao) against him at San Mamés. He was at the end of his playing career and I was at the beginning of mine. Then he was the Espanyol manager and I faced him several more times. Now I play under him at Tottenham and I really want to give my best."
The Spaniard added to Onda Cero: "The truth is that Chelsea have been after me for a long time but at the end you know how this works. At the very last minute Pochettino called me and convinced me [to join Tottenham]. The Tottenham project is impressive. They have done very well in the last few years and I think I fit very well with this project. I think I can help them a lot,"
Llorente is yet to play a Premier League game either for Swansea or Tottenham this season after he fractured his arm at the end of June while on holiday. The Spaniard was therefore doubly delighted as he hopes that the minutes played against Dortmund could serve him well in regaining his best form as soon as possible.
"I'm very happy to have played my first minutes in the Tottenham shirt. I was really looking forward to playing again," the former Swansea striker added.
"It has not been an easy pre-season after I broke the arm but I'm little by little getting myself better. I'm already fit to play but I still do not have the arm at 100%. I'm happy to be able to play again. Now it's vital to get some more minutes in order to get to the same level of my teammates to try to help Tottenham."