Clinic26 will provide sexual health services and emotional support to men of all ages at the Ambrose Centre at the Royal London Hospital.
On average, 12,000 men are raped and 72,000 are sexually abused each year, Home Office statistics show.
The clinic has been set up in partnership with Survivors UK.
One sexual abuse victim said he was thrilled when he heard the clinic was opening.
Jay - not his real name - said he was sexually assaulted by a nurse when he had a routine health screening in 2013.
"I was hugely distressed by it (the assault). It took me nine months to go back for another screening," he said.
Initially, the health trust did not take action against the nurse, but it eventually reinvestigated before another victim came forward. The nurse was found guilty and was jailed for two years.
Jay said he wanted to go to a place "where people knew" he'd been sexually assaulted and he didn't have to disclose it to see the reaction.
Andy Williams, consultant physician at The Royal London Hospital, said: "We need to break the taboo that allows men to suffer in silence and this clinic is the beginning of what we hope will be a valued support resource for men in east London."
Alan Robertson, Independent Sexual Violence Advisor at Survivors UK, said: "Going to a sexual health clinic can be a daunting prospect for anyone, but especially so for someone who has experienced trauma or an abuse of power."
The clinic will run on the afternoon of the last Monday of each month.

A demonstration was held at the weekend by animal rights campaigners in Derby over the planned facility near Foston.
Midlands Pig Producers (MPP) said allegations its pigs would be kept in cramped conditions were untrue.
The farm would hold 2,500 sows and 20,000 piglets and use biogas from the slurry to produce electricity.
MPP has finished giving extra information to Derbyshire County Council as part of the planning process.
It said it had addressed concerns about animal welfare and emissions.
A company spokesman said: "We are astonished at some of the highly misleading claims and accusations.
"Claims that pigs will be crammed into narrow crates are simply not true.
"Our acclaimed 360 Farrowers were named because the sow can turn around 360 degrees at will.
"We urge people to either contact us, or refer to the planning application so that they may ascertain the facts of the matter for themselves."
About 100 animal rights protesters marched through Derby on Saturday claiming the large-scale development would be cruel to pigs.
Critics said that the only time the pigs would see the outside world would be on their way to slaughter.
It has also been claimed the site could put small-scale farmers in the area out of business.
MPP said the farm would observe the highest welfare standards and pointed out there was already a unit in the UK containing 3,500 sows.
South Derbyshire District Council handed over duties for dealing with the application to the county council because of its waste implications.
If planning permission is given, construction on the farm will take about a year.
Support groups have set up what they say is the first UK clinic to offer support for male sexual abuse victims.
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The company behind a proposed large-scale pig farm in Derbyshire has hit out at "misleading" claims surrounding its plans.