The 23-year-old striker passed a medical at the club's Melwood training ground on Tuesday.
He briefly flew back to his homeland to say an emotional goodbye to fans in Madrid before arriving back on Merseyside on Wednesday to complete the formalities of the transfer.
Torres, speaking through an interpreter, said: "I'm very happy to be joining the club.
"It is a fantastic opportunity to be joining one of the best clubs in Europe with a fantastic history.
"You don't get opportunities like this every day of your life."
Asked what impact manager Rafael Benitez had on his decision the Spain striker said: "It was important, the confidence shown in me by him.
"When you hear a club like Liverpool is interested in you it is something that fills you with a lot of surprise and a lot of pride."
Torres insisted he was ready to work extremely hard to live up to his high price tag.
He told Sky Sports News: "The figures that have been mentioned are bound to bring an added pressure, but when you sign for a club like Liverpool you've got to bear pressure.
"I know the demands are high but I believe in hard work and think I can work hard to fulfil those expectations."
Asked whether it would be hard to adapt to the English top flight, Torres added: "Liverpool are a slightly different case, I have spoken to my team-mates who have come from the Spanish league so that will help with settling in."
Torres would not be drawn on reports that Chelsea had been interested in signing him last summer.
He said: "I don't think it does any good to speak about what happened in the past. As soon as I heard of Liverpool's interest that was the only club I wanted to consider."
Torres expressed his determination to settle in as soon as possible and secure a regular first-team place.
"I will be working from day one and getting to know my team-mates more closely," he said.
"You have to make sure you are in a position to make choices difficult for the manager as all my team-mates here are of the highest quality.
"Liverpool are the type of club that aspire to win trophies and I will certainly be trying my hardest and doing my little bit to try to improve that record, improve our chances and improve the team a little."
He has also been handed the club's famous number nine shirt worn by the likes of Ian Rush and Robbie Fowler, but is adamant that will also spur him on.
Torres, who will play alongside the likes of Jose Reina and Xabi Alonso, said: "Hopefully I can settle as quickly as possible. It will be a help that there are so many Spanish speakers here and also the manager.
"I'll be able to understand them from the word 'go' and let's hope the settling in period is as short as possible.
"I don't see it as a pressure. It's a good responsibility and at the same time, it's a real privilege to have the opportunity to wear the shirt number.
"The fact that Liverpool have given me that number shows they've got a lot of confidence in me and they've got high hopes I will succeed.
"I just hope that I can do well over a good number of years at this club and be remembered in the same way as the guys that have been mentioned.
"I hope I can repay the confidence they've shown in me on the field in seasons to come."
While many new arrivals claim to have followed their new club all their life, there is no doubting Torres is genuine.
His friends have Liverpool tattoos and he was also pictured with 'We will never walk alone' on the inside of his Atletico Madrid captain's armband last season.
He added: "A group of my mates and I are all Liverpool fans and we have been for some years.
"A few years back, my friends each got a tattoo on their arm but obviously as a football player, I couldn't really get that tattooed on my arm.
"So on my last birthday they gave me the present of the armband with it written on the underside and it's 'We'll never walk alone'.
"This club is well capable of winning the Premiership and other trophies as they have proved in the past and recent history.
"We will be fighting on all fronts this year."
Benitez himself was doubly impressed by Torres' desire to move to Anfield and was pleased with reports from his players returning from Spain duty.
He said: "There is the anecdote with the armband and, maybe I shouldn't say this, but he was talking with some of his team-mates in the national team.
"He said 'ok, if I leave Atletico Madrid I would like to go to Liverpool. Say to Rafa, please say to Rafa!'
"The last season, we knew that (Dirk) Kuyt was our target and this year (Torres) was our target.
"After we reached an agreement with the club, they received a big offer, bigger than our offer, but the player said he wanted to go to Liverpool and he didn't want to hear anyone just to come here. That's the positive thing for me."
Benitez added: "I am really pleased. We were working hard to find the best players for us.
"We know that it is expensive but not as much as people say. We are bringing in a young player with a great future."
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