The former Monaco and Juventus forward was allowed to leave the Spanish Champions despite having one year remaining on his contract.
Ã¢â‚¬Å“It is an honour to play for the New York Red Bulls,” Henry said after completing the move.
Ã¢â‚¬Å“I am fully aware of the teamÃ¢â‚¬â„¢s history and my sole goal during my time here is to help win the club its first championship.Ã¢â‚¬Â
Henry has endured a hugely disappointing season, falling behind Spanish youngster Pedro and then being part of the French side that failed to progress past the group stages at the World Cup.
The 32-year-old has had a very successful career, scoring 226 goals in 370 games for Arsenal and winning two Premier League titles and enjoying three FA Cup triumphs.
The illusive Champions League winnerÃ¢â‚¬â„¢s medal arrived in his second season at Barcelona after a Ã‚Â£16.1m deal in June 2007.
He scored 49 goals during his three seasons in Spain, winning La Liga twice, the Champions League and also the UEFA Super Cup and FIFA Club World Cup.
The Frenchman also won the World Cup in 1998 and the European Championship in 2000, scoring 51 goals in 123 appearances for his country.
Ã¢â‚¬Å“This marks an exciting new chapter in my career and life,” Henry continued.
Ã¢â‚¬Å“Knowing Red BullÃ¢â‚¬â„¢s significant commitment to soccer locally and internationally, I am confident that my team-mates and I will succeed.Ã¢â‚¬Â
Ironically, Henry could well play his first game for the MLS side against Tottenham in a friendly on 22 July.
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