The study examined footage of the footballer before and after 2007, the year the Beckhams moved to Los Angeles.
David dropped his H sounds at the start of words far less often than before the move to the US, the study found.
And in a separate video study of wife Victoria, the ex-Spice Girl was found to be "definitely getting posher".
A university spokesman said the research was part of a study into "how changing circumstances affect the way we pronounce words".
Researchers contrasted the way Beckhams spoke before and after their move to the US, when David signed for Los Angeles Galaxy.
Charles Boorman and Alix Roberts looked at changes in David's speech, while Naomi Proszynska and James Pickett investigated how Victoria spoke.
The research revealed that David dropped the H in words such as "him" and "has" 80% of the time before the move to the US, but only 20% of the time afterwards.
Mr Boorman said it was "clear that Becks, once a broader Cockney, nowadays speaks with more of a standard English accent".
"In fact, he's even hyper-correcting himself, because he puts Hs into words when it's not really required - in America, they use the H sound more, which explains how he acquired it.
"But my guess is that his dropping of those Cockney vowels was linked to his ambassadorial role for the Olympics and his subsequent high social status."
Victoria - dubbed Posh Spice during her days with the Spice Girls - was found to correctly pronounce Ls in words such as "all" 25% of the time in 1997, with the figure rising to 46% in 2012.
"All" can be pronounced "awe" by "working-class people in the south-east of England", the researchers said.
Source: University of Manchester
Ms Proszynska said: "In 1997, her speech resembled what we associate with the classic Essex girl but, by 2012, her speech no longer so strongly represented her Essex roots.
"We think this may be connected with the fact that she's forged a different career as a widely respected fashion designer."
Linguistics lecturer Dr Laurel MacKenzie said pronunciation was not "static" in adults.
"The general assumption is that once we pass puberty our way of speaking is fixed," she said.
"But recent research has revealed the extent to which we can be chameleons in the way we speak, even into adulthood.
"Factors such as social mobility and geographical location can have an impact on the way adults pronounce words."
David Beckham has changed his speech over the past decade to "sound less working class", University of Manchester academics have concluded.