Liverpool have confirmed the agreement and the controversial striker will now leave Anfield next week as the game's third-most expensive player, with Barca saying he will sign a five-year deal.
In a statement, the Reds said: "Liverpool FC confirms that Luis Suarez will be leaving after a transfer agreement was reached with FC Barcelona. The player now has permission to complete the usual formalities, which will then conclude the transfer,
"We would like to thank Luis for his contribution and the role he played in helping bring Champions League football back to Anfield.
"Everyone at Liverpool Football Club wishes Luis and his family well for the future."
Officials of the two clubs began talks over a week ago which were productive from the start, with the Catalans agreeing to meet the Uruguay international's buy-out clause.
Suarez asked Liverpool fans to try to understand it had always been his dream and ambition to play in Spain.
"It is with a heavy heart that I leave Liverpool for a new life and new challenges in Spain," said the 27-year-old, whose move to Barcelona takes him closer to his wife Sofia's family.
"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."
Rodgers said the club and the player have benefitted from his time at Anfield.
"Luis is a very special talent and I thank him for the role he has played in the team over the past two years during my time at Liverpool," he said.
“I think he would be the first to accept he has improved as a player over that period along with the team and has benefitted from being here as we have benefitted from him.
“The club have done all they can over a sustained period of time to try and keep Luis at Liverpool but it is with great reluctance that following lengthy discussions we have eventually agreed to his wishes to move to Spain. We wish him and his young family well and will always consider them friends.
"We are focused on the future, as we strive to continue with the progress we have made and build on last season's excellent Barclays Premier League campaign.
"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
"If there is one thing the history of this great club teaches us is that Liverpool FC is bigger than any individual. I hope our supporters continue to dream and believe we are moving forward. With continued improvement and progression together we will bring the success we all crave and deserve.”
Barca, meanwhile, confirmed Suarez 'will be travelling to Barcelona next week for a medical, to sign his five-year contract and to be officially presented to the media and fans as an FC Barcelona player'.
The 27-year-old was expelled from the World Cup last month and handed a nine-match international ban as well as a four-month sanction from any football activity for biting Italy defender Giorgio Chiellini.
He appealed against FIFA's ruling, but was unsuccessful and he will not be able to train with his new team-mates until the end of October.
Suarez's lawyer said on Friday that he will appeal to the Court of Arbitration of Sport against the suspension, though this has not been confirmed by the player or his new club.
That move would represent a gamble. If CAS puts the suspension on hold, that would allow Suarez to train with Barca and potentially start the new season. But if CAS subsequently rejected the appeal and upholds FIFA's decision, Suarez would find himself suspended for four full months of football, rather than the off-season and first couple of months of the new campaign.