The 29-year-old has signed a four-year deal with the Spanish giants and was unveiled at a press conference at the Nou Camp.
Barca's medical team spent the day putting Henry through his paces at a Barcelona hospital.
And team doctor Ricard Pruna confirmed that he had successfully passed the tests.
Henry was formally presented to the press at 5pm BST - and signed his contract in front of TV cameras.
He leaves the Gunners as the club's record goalscorer after netting 226 goals in 364 appearances.
Henry's arrival gives Barca coach Frank Rijkaard a wealth of attacking options next season, with the likes of Samuel Eto'o, Ronaldinho, Eidur Gudjohnsen and Lionel Messi already on the books.
The classy Frenchman said: "I am really pleased to be here. It has been a long chase but I'm finally here and happy to be here and I can't wait to go out there and show what I can do.
"Hopefully I can be a great asset for the team.
"I haven't set any targets or objectives. It has to be a club target.
"Barcelona is always a club that wants to win everything. I am going to try my hardest to help as much as I can.
"It has to be a team effort right from the start."
A Champions League winner's medal was the major omission from Henry's CV while at Arsenal - who lost to his new team in the 2006 final - but the Frenchman said he was not prioritising anything at the Nou Camp.
"I have to live and breathe Barcelona. It is dream for everyone to win the Champions League and I'm sure it will be the dream of Barcelona to win it again next season," added Henry on Sky Sports News.
"It is the only thing I didn't win [at Arsenal] but the most important thing is that Barcelona is successful and they win silverware."
Despite rumours of an approach from the Catalan giants last summer, Henry said he had not spoken to coach Frank Rijkaard until he was given permission once both clubs had agreed a deal.
"We had a chat only when I was allowed to speak to Barcelona. What we said to each other will stay with each other," he explained.
Henry also stressed there would be no rivalry with fellow striker Samuel Eto'o, who is a good friend.
"The relationship I have with Samuel is from a long time ago," Henry added. "I know a lot of players in the team but on top of that Samuel and I have been really close in the past two years.
"He came to see me at my house when I got injured a few months ago and I came to see him when he had an operation (in the early part of last season).
"I know you guys (the media) would not like us not to be friends but we are friends."
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