The 32-year-old is one of a number of players to have rejected a move to the champions, instead deciding to join London rivals Spurs from Swansea City in a £14m deal.
Llorente admits that his decision to choose the Lilywhites was down to Pochettino, who he has previously come up against during the Argentine defender's playing days at Espanyol.
"At the very last minute, Pochettino called me and convinced me [to join Tottenham]," he told the Daily Mail. "The truth is that Chelsea have been after me for a long time but at the end you know how this works.
"I am 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. It is clear that Pochettino played a very important role in the decision.
"I made my first-team debut [for Athletic Bilbao] against him at San Mames. He was at the end of his playing career and I was at the beginning of mine. Then he [became] 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."
Llorente, who netted 15 times in his maiden Premier League campaign with Swansea, came off the bench for the final three minutes against Borussia Dortmund for his Spurs debut in midweek.