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The Uruguayan, 27, who is serving a four-month ban for biting Italy's Giorgio Chiellini during the World Cup, will sign a five-year deal.
Suarez, who scored 31 league goals last season, will travel to the Spanish club next week for a medical.
"Luis is a very special talent and I thank him for the role he has played," said Liverpool boss Brendan Rodgers.
Suarez - last season's Premier League top scorer and winner of the PFA and Football Writers' Player of the Year awards - signed for Liverpool from Ajax in 2011 for £22.7m, and had four years left on his contract.
The move to Barcelona takes him closer to his wife Sofia's family.
"I hope you can all understand why I have made this decision," said the striker, who is banned from "all football-related activity" until the end of October as he serves his third suspension for biting an opponent.
"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."
Suarez thanked the "wonderful" Liverpool fans in a letter - tweeted from his account - for supporting him "in good times and bad".
When he is eventually eligible to play again, Suarez is expected to wear the number nine shirt in a formidable Barcelona front line including Argentine Lionel Messi and Brazilian Neymar.
The club is looking to rebuild under new coach Luis Enrique after its first season without a major trophy in six years.
If the transfer fee is confirmed at £75m, it will be the third biggest in  football history after Gareth Bale (£86m Tottenham to Real Madrid, 2013) and Cristiano Ronaldo (£80m Manchester United to Real Madrid, 2009)
"It is with a heavy heart that I leave Liverpool for a new life and new challenges in Spain," said Suarez.
"Both me and my family have fallen in love with this club (Liverpool) 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."
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In his statement, released on Liverpool's official website, Suarez concluded: "Thank you again for some great moments and memories. You'll Never Walk Alone."
The transfer means Liverpool do not have to deal with the fall-out from a Suarez suspension for the second season running.
They supported the player after another biting attack - on Chelsea's Branislav Ivanovic at Anfield in April 2013 - which led to a 10-game ban, and he signed a new contract in December.
"The club have done all they can over a sustained period of time to try to keep Luis at Liverpool," added Rodgers.
"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."
Suarez leaves Liverpool having scored 82 goals in 133 appearances, but also serving two bans - he was given an eight-game suspension in for racially abusing Manchester United's Patrice Evra.
He had tried to force a move away last summer, prompting an ill-fated £40,000,001 bid from Arsenal to trigger a release clause.
Meanwhile, Barcelona face a logistical conundrum regarding his presentation as their player - usually done at the Nou Camp which is opened up to fans - as his worldwide suspension extends to entering any football ground.
They are permitted to buy and sell players this summer after football's governing body Fifa suspended its 14-month transfer ban on the club pending an appeal.
Barcelona were given the 14-month suspension after being found to have breached rules on signing international players under the age of 18.

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Liverpool have agreed to sell striker Luis Suarez to Barcelona for a fee thought to be about £75m.
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After nine months, 380 games and more than 1,000 goals, another Premier League season grinds to a halt on Sunday.