The Uruguayan striker will not be able to make his debut for the Catalans until November due to the four-month worldwide ban from football activities Fifa imposed on him after he bit Giorgio Chiellini at the World Cup.
"It is with a heavy heart that I leave Liverpool for a new life and new challenges in Spain. Both me and my family have fallen in love with this club and with the city.
"But most of all I have fallen in love with the incredible fans. You have always supported me and we, as a family, will never forget it, we will always be Liverpool supporters.
"I hope you can all understand why I have made this decision. This club did all they could to get me to stay, but playing and living in Spain, where my wife's family live, is a lifelong dream and ambition. I believe now the timing is right.
"I wish Brendan Rodgers and the team well for the future. The club is in great hands and I'm sure will be successful again next season.
"I am very proud I have played my part in helping to return Liverpool to the elite of the Premier League and in particular back into the Champions League.
"Thank you again for some great moments and memories. You'll Never Walk Alone."
Liverpool coach Brendan Rodgers added: "The club have done all they can over a sustained period of time to try to keep Luis at Liverpool. It is with great reluctance and following lengthy discussions we have eventually agreed to his wishes to move to Spain for new experiences and challenges. We wish him and his young family well; we will always consider them to be friends.
"If there is one thing the history of this great club teaches us, it is that Liverpool FC is bigger than any individual. I hope our supporters continue to dream and believe that we are moving forward and with continued improvement and progression, together we will bring the success we all crave and deserve."
Named the PFA Player of the Year last season, Suárez leaves English football after three-and-a-half turbulent years in which he served 19 matches worth of suspensions without ever getting sent off.
In December 2011, he was found guilty of racially abusing Manchester United left-back Patrice Evra and last year he bit Chelsea defender Branislav Ivanović.
Suárez only won the League Cup with Liverpool, however his vibrant form in the 2013-14 campaign helped the club up to second only to Manchester City, as the Reds came agonisingly close to a first title since 1990.
Alongside Neymar and Lionel Messi, Suárez will form a daunting South American attacking triumvirate and his arrival at Camp Nou comes the day after Barcelona sold Alexis Sánchez to Arsenal.