The 32-year-old Henry announced on Wednesday that he had agreed to leave Barcelona to take up a "multi-year" deal with the Red Bulls.
"This marks an exciting new chapter in my career and life," he said in a statement released by the New York team.
The former Juventus and Arsenal forward will join England's Beckham and former Sweden international Freddie Ljungberg among the league's 'designated players' who have most of their salary paid outside of their team's salary cap.
Henry is expected to play his first match next week when the Red Bulls host Tottenham Hotspur at their new stadium.
"It is without question that Thierry Henry is one of the most successful and recognisable soccer players over the past 15 years," said Dietmar Beiersdorfer, head of New York's owners, Red Bull Global Soccer.
"We are thrilled that Thierry has decided to come to New York to help the Red Bulls compete for championships this year and for years to come. His international pedigree is second to none and he is a proven winner."
The Red Bulls have recently moved into a new, purpose-built stadium in New Jersey but have yet to win an MLS title and are pinning their hopes on Henry.
"I am fully aware of the team's history and my sole goal during my time here is to help win the club its first championship," Henry said.
Henry started out at Monaco and Juventus before spending eight successful seasons with Arsenal, helping the London club to win two Premier League titles and three FA Cups.
A World Cup winner with France in 1998, he joined Barcelona in 2007 and was the team's top scorer in his first season but he has had a difficult last 12 months, struggling to cement a regular first-team spot because of injuries.
Henry almost quit international football after he was heavily criticised for his handball that allowed France to qualify for the World Cup ahead of Ireland.
He stayed on to be part of the French team that failed to progress past the pool stage in South Africa after highly-publicised internal squabbling.
Henry still had a year to run on his Barca contract but the Spanish giants agreed to release him early.
"Thierry is not only a world-class player who will undoubtedly improve our squad, but he has shown most importantly throughout his career that he is a winner," Red Bull general manager Erik Soler said.
"He has made it clear to us that he is committed in the short and long term to help in our vision of making our organisation the premium franchise in Major League Soccer."