The forward leaves after three and a half years at Anfield.
Suarez joined Liverpool from Ajax in the winter of 2011 and became an instant hit at Anfield, and had a record-breaking season for Liverpool last term as he scored 31 goals for the club as they came within two points of winning the Premier League title, and he picked up both the Players and Football Writers Player of the Year award.
However, his time at Anfield has not been without controversy. He was banned for eight games in 2011 after being found guilty of racially abusing Manchester United's Patrice Evra, and a season later he was banned for 10 games for biting Chelsea defender Branislav Ivanovic.
The summer that followed saw Suarez first try to instigate a move away from the Premier League, and then one to Arsenal but the Reds refused to sell.
After returning from his ban last season, Suarez kept himself out of trouble as Liverpool progressed remarkably from seventh to second but at this summer's World Cup he bit Giorgio Chiellini, which means he won't be able to play any football until November.
During his time on Merseyside, Suarez's hard work and win at all costs mentality made him a hit with the fans, as well as his footballing ability. He managed to find the net on 82 occasions in 133 appearances.
Liverpool manager Brendan Rodgers wished Suarez the best in his departure for Barcelona, and is confident Liverpool can still improve despite the loss of the Uruguayan.
He told the club's website: "I think he would be the first to accept he has improved as a player over that period, along with the team and has benefited from being here, as we have benefited from him.
"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.
"I am confident we will improve the team further and will be stronger for this coming season, when we will be competing on all fronts; domestically and in the greatest club competition in the world, the Champions League.