The former England captain told Reuters in an interview that he would also not rule out his veteran former Manchester United team-mate Ryan Giggs ending up with him on the other side of the Atlantic as well.
France striker Henry, 32, announced earlier that he was leaving Barcelona for a multi-year deal in New York.
"I think it's great," said Beckham, speaking to Reuters Television after a worldwide interview with questioners from 18 countries on five continents through a live link-up on yahoo.com.
"Thierry joining the Red Bulls is great. I knew that he was interested in coming to the MLS because we've talked many a time about it and I've known for a while certain things," added the 35-year-old LA Galaxy midfielder.
"Thierry going there can only be good for the sport because it raises the profile, gets people talking about the MLS again and it makes it bigger.
Beckham, who has a record 115 caps for an England outfield player but missed the World Cup through injury, joined the Galaxy from Real Madrid in a mega-money move in 2007 and still has two years remaining on his contract.
Henry won the World Cup with France in 1998 and joined Barcelona from Arsenal in 2007, helping them win the Spanish, European and World Club titles.
GIGGS MOVE
"For a player of his calibre and a name that he's got around the world and in the sport, for him to be going to New York and playing for Red Bull is exceptional," said Beckham.
"I can't wait to play against him. We are good friends and get on well. He's an exceptional talent."
Giggs, 36, was quoted in the British media as saying he could end his career in America although he still had a year left at United and might be too old by then. Beckham disagreed.
"I think Ryan has looked after his body so well for many years and that's the reason why he's playing at such a high level still at his age," he said.
"I think if he feels like he can still do it, he will do that. It doesn't matter what age you are. If a Ryan Giggs and a Thierry Henry comes over and plays in the MLS it's great for the sport."
Beckham said the U.S. team's performances in the World Cup, reaching the last 16, had also have given football a boost in America.
"I think it did a lot. I heard 25 million watched the final in America, so that's saying something. For a country where soccer is not the number one sport, I think that's exceptional," he said. "The interest is there."
"They had some great players there and some great moments, scoring in the last minute to go through to the next round. Things like that. American people love the excitement and I think that helps the sport in the U.S."
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