The 33-year-old former Stevenage and Fleetwood player made 52 league starts for Cambridge over the past two years.
He has signed a one-year contract with Mark Cooper's side.
"I was involved in two successful promotion campaigns [with Stevenage and Fleetwood]. I'd love to have a third," Roberts told BBC Radio Gloucestershire.
Speaking of the former Crewe youngster, who has also played for Accrington, Rovers boss Cooper added: "He is a good, solid defender and he'll give our younger players that little bit of guidance."
Cambridge chief executive Jez George told their club website: "Since arriving at the club, Mark has been an absolute professional, on and off the pitch."
On Wednesday, Forest Green confirmed the departure of midfielder Rob Sinclair by mutual consent.
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The 33-year-old made a total of 12 Test appearances and played a vital role in the 2010-11 Ashes victory in Australia.
"After 16 enjoyable years I feel that now is the right moment to call time on my playing career," the Surrey player wrote on Twitter.
"Unfortunately injury has hampered me throughout my career and now plays the leading role in my decision to retire."
Tremlett has been affected by back and knee injuries in recent years and has been restricted to three Championship appearances for Surrey this season.
"My body, and back in particular, can no longer withstand the vigour of performing at the level required to play professional cricket," he said.
"After taking specialist advice this latest injury means that I will not be able to carry on.
"I have always tried to give 100% commitment and effort whenever I have played but no longer feel that this is possible."
Southampton-born Tremlett, who began his career at Hampshire before moving to Surrey in 2010, took 53 wickets at an average of 27 in his 12 Test appearances for England.
The most significant, however, were the 17 in three matches as England won the Ashes in Australia in January 2011.
He also played 15 one-day internationals and one Twenty20 match for England, with his last appearance for the national team coming in the first Test against Australia in November 2013.
"Wearing the Three Lions was the pinnacle and I enjoyed every minute of the challenge, experience and ultimately the success that the team had," he added.
"I have been extremely fortunate to have enjoyed such a fantastic and memorable career and lucky enough to play with and against some of the best players in the world."

The 65-year-old was found dead in the garden of his gated home in South Weald in June 2015.
Although Essex Police originally thought he died of natural causes, it emerged he had been shot six times.
Police said they had questioned a man originally from Tyneside but currently living in southern Spain.
The force says the man was not arrested but volunteered to be interviewed at a police station in the UK. The force did not specify which police station he was interviewed at.
The interview took place on Saturday morning.
An inquest into Palmer's death concluded he was unlawfully killed. Police have said his shooting had "all the hallmarks of a professional hit".
Palmer, once described as Britain's richest criminal and thought to have been worth £300m, got his nickname after he was arrested on suspicion of melting down gold from the Brink's-Mat robbery, although he was never convicted.
The robbery in 1983 took place at Heathrow Airport when £25m worth of gold was stolen. At the time it was the biggest robbery to have ever taken place in the UK.
The former scrap metal dealer, from Olton, near Birmingham,  who was one of seven children, was said to have melted the metal down in the back garden of his mansion at Lansdown near Bath.
However, he denied knowing it was stolen and was acquitted in 1987, blowing kisses to the jury from the dock when the verdict was delivered.
Worth about £500m in today's prices, most of the gold has never been recovered and the case remains open.
In 1997 Palmer was arrested in Tenerife, and returned to the UK to face charges related to a large-scale timeshare fraud.
In May 2001 he was sentenced to eight years in prison and ordered to pay a record confiscation order of £33m.
Forest Green Rovers have signed defender Mark Roberts after his contract at Cambridge United was cancelled by mutual consent.
[NEXT_CONCEPT]
Former England fast bowler Chris Tremlett has announced his retirement from all forms of cricket.
[NEXT_CONCEPT]
A 50-year-old man has been questioned on suspicion of the murder of notorious criminal John "Goldfinger" Palmer, detectives have said.