The 37-year-old had hoped to be named as one of three over-age players but has not been selected by Olympic team coach Stuart Pearce.
It is understood Ryan Giggs, Craig Bellamy and Micah Richards will be the three over-age players confirmed by Pearce next week.
Beckham said in a statement: "Everyone knows how much playing for my country has always meant to me, so I would have been honoured to have been part of this unique Team GB squad.
"Naturally I am very disappointed, but there will be no bigger supporter of the team than me. And like everyone, I will be hoping they can win the gold.
"As a Londoner I was really proud to have played a small part in bringing the Olympics to my home town as part of Seb's [Coe] team and I can't wait for the Games to begin and will enjoy every moment along with the rest of Great Britain."
Beckham is understood to have been told by Pearce that he had chosen to pick Richards instead because he wanted stronger defensive options.
The former England midfielder had been on the 35-man shortlist and Pearce had flown out to the United States to watch him in action for the Los Angeles Galaxy. The player could also point out that he would have at least been match-fit while all the other players would be entering the tournament after the summer break.
Giggs and Bellamy were widely expected to be included but the call-up of Richards is also as much of a surprise as the Manchester City defender being left out of England's Euro 2012 squad - after which he refused to go on standby for the European Championship.
Other under-23 players who are almost certain to be confirmed by Pearce include Arsenal's Aaron Ramsey and Tottenham's Gareth Bale.
Manchester United had told the FA in May that they did not want any of their over-age players apart from Welsh winger Giggs to be considered for selection. The club ruled out Pearce picking Rio Ferdinand, Paul Scholes and Jonny Evans for the Olympic tournament.
It means United players Tom Cleverley and Chris Smalling, who both missed Euro 2012 through injury, may be part of the Olympic squad.
England great Peter Shilton understands Pearce's decision to omit Beckham as he believes the 37-year-old could have struggled to last the pace.
Shilton, England's most capped player with 125 appearances, believes Beckham would have struggled with the physical demands of competing at the Games.
"I've not been watching David play in the States but it's a different level of football over there," Shilton told Sky Sports News.
"Stuart Pearce wants to do well and win the tournament. To do that you must win so many games in so many days and the older you get the less you can do that.
"David might play the first game well, but then the second game becomes a bit harder.
"He's been a fantastic player over the years, certainly when he was at his peak, but he's nowhere near the player he was.
"It would have been great from a publicity point of view, but Stuart Pearce obviously feels he'd struggle in that type of tournament.
"You have to respect Stuart's opinion but I've always had the utmost respect for David as a person and a player."