The promoted Premier League club have announced on their official website that the 27-year-old central defender has moved to Elland Road on a four-year contract.
The Spain international had been on the books of Sociedad since the summer of 2017 when he joined from Spanish and European giants Real Madrid.
The centre-back could not make a massive impact during his time at Madrid, but he established himself as one of the best defenders in La Liga during his time at Sociedad.
Llorente is overjoyed to have moved to Leeds, and he has explained his decision to pick the West Yorkshire club as his destination.
The centre-back said: “I’m very happy to be here and I’m looking forward to meeting my teammates and manager as soon as possible.
“I have a lot of energy and with my abilities I think I can help add to the team and this is the goal for me.
“I was happy when Leeds United got back to the Premier League and to be here is an honour and its a good challenge for me.
“I talked with Pablo Hernandez and he told me about the team, the city and all of the things he said were good, so the decision for me was very easy and I am excited to be here.
“For me the Premier League is the competition that is the most important in the world of football and it is a challenge to be here and Im looking forward to getting started and helping my teammates.
“Marcelo Bielsa was also a key factor, for me he is the greatest manager in the world and it is an honour, I’ve come to learn as much as possible from him.”