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."

Officials say 108 tons of corn will be delivered by the end of the weekend.
Last month, eight people were killed in Oaxaca in clashes between the demonstrators and police.
The protesters oppose reforms that allow the federal authorities to remove teachers who fail evaluation exams.
Members of the CNTE union, which has a history of radical activism, have been blocking roads in Oaxaca and other states ever since the union leaders were arrested in early June.
The roadblocks have prevented food deliveries to some remote areas in the region, the government says.
"There are no products," says Araceli Hernandez Ramirez, manager of a grocery store in Puente de Coyula.
She says she has no rice, corn or flour to sell to her customers. "They go home empty-handed," she said.
In a strongly worded message on Friday, Interior Minister Miguel Angel Osorio Chong said the unrest had hurt millions of people and "the blockades and damages to the citizenry must end".
"The time is up," he said, warning that "the necessary decisions will soon be taken to allow transit on strategic roads".
The CNTE union opposes education reforms introduced by President Enrique Pena Nieto in 2013.
The changes include new measures to assess teachers' performance.

The 29-year-old finished 11th in the -94kg class for Armenia, where he was born, but has since switched to represent the United States.
A retest of his 2012 sample revealed the presence of a steroid.
A total of 43 weightlifters have now failed retests from the 2008 and 2012 Olympic Games.
Six more competitors from Vardanian's event at the London Olympics are already facing disqualification after retests found steroids.
Vardanian was previously banned for six months in 2009 after testing positive for cannabis.
David Beckham has changed his speech over the past decade to "sound less working class", University of Manchester academics have concluded.
[NEXT_CONCEPT]
Mexico's air force has been flying tons of grain into Oaxaca state in the south of the country to deal with dwindling food supplies caused by roadblocks set up by protesting teachers.
[NEXT_CONCEPT]
American weightlifter Norik Vardanian has tested positive for a banned substance in a sample he gave while competing for Armenia at London 2012.