The deal, thought to be worth about £16m to the Gunners, is subject to the Frenchman, 29, passing a medical, which is set to take place on Monday.
Barca announced on their website that they expected Henry to agree terms on a four-year deal within hours.
"I still must pass a medical on Monday but yes, I have chosen Barcelona," he told French sports daily L'Equipe.
Earlier, Barcelona revealed that they were close to bringing Henry to the Nou Camp, with vice-president Ferran Soriano telling Spanish sports newspaper Marca that talks were at an "advanced" stage.
Soriano added it was "the wish of all parties" for an agreement to be reached for the transfer of Henry.
He also insisted that Barcelona waited for the green light from Arsenal before making a move for the France international, who is the club's all-time record goalscorer.
"We don't want to point a gun at anybody," said Soriano. "We have good relationships with the European clubs."
Henry, who only agreed a lucrative new deal with Arsenal 12 months ago, also confirmed his exit in The Sun newspaper.
In an open letter, he blamed the shock departure of Gunners vice-chairman David Dein and continuing doubts over the future of manager Arsene Wenger as the main reasons for his decision to leave.
"Arsene has been part of my life for as long as I can remember," he wrote.
"Unfortunately and understandably, he has said that at this moment he will not commit to the club past the expiration of his current deal, which finishes at the end of the coming season.
"I respect his decision and his honesty but I will be 31 at the end of next season and I cannot take the chance to be there without Arsene Wenger and David Dein.
This is solely my decision, no-one has forced me to do anything and I will represent myself in this transaction. I feel it is something I just had to do."
Henry, who has also been linked with European champions AC Milan, has also revealed why he decided to move to the Nou Camp ahead of other possible destinations.
"Barcelona are a wonderful club steeped in tradition and play beautiful football. I'm sure I will be very happy there," he continued.
"But I will miss the Arsenal fans dearly, they have supported me through thick and thin.
"They will always be in my heart, as will all the fans who make the game here so special. I will always have a special bond with Arsenal Football Club."
Arsenal's 1971 League and FA Cup winning captain Frank McLintock was surprised Henry cited former vice-chairman Dein as a reason for leaving.
He said: "I can't see the relevance of David Dein's departure. I don't know how a player can get caught up with a director's departure and that making a difference to a player's performance.
"I'm sure he was a great ally to Arsene Wenger but I don't see how a player comes into contact with a director day after day.
"I've never heard such talk in my life before."
The Scot, however, was lavish in his praise of Henry's performances throughout his Arsenal career.
He added: "He's probably been the finest player Arsenal have ever had so you can't dismiss five or six great seasons that he gave us.
"I think the fans should leave with a warm feeling for Thierry Henry. He deserves it - he has been magnificent
Henry began his career as a winger with Monaco in 1994 - under the supervision of current Arsenal boss Wenger.
He was in France's 1998 World Cup-winning squad and went on to join Juventus the following season.
But his time in Turin was a largely unsuccessful one and the player was soon heading to north London, with Wenger keen to get the best out of the prodigious talent.
The France international has since blossomed into one of the greatest talents in world football.
He helped Arsenal to two league titles and three FA Cups and led the Gunners to the finals of the 2000 Uefa Cup and 2006 Champions League.
In February 2006, he became the first Arsenal player to score over 200 goals for the club, with a strike against Birmingham, and has bagged a club record 226 goals in 364 appearances for the Gunners.
His consistency in front of goal ensured he finished as the Premier League's top scorer on four occasions.
He has won the Professional Footballers' Association player of the year title on two occasions and the football writers' player of the year three times. He has also twice finished runner-up in the Fifa world player of the year
bbc.co.uk
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