Meanwhile, the law firm that represents Testino has said they were equally "shocked by the allegations" and that the employees coming forward "could not confirm any of the claims".
Testino, who is known for taking iconic photographs of Diana, Princess of Wales, months before her death, and Weber have been suspended from working with publications like Vogue and GQ, reports The New York Times.
He goes on to clim that Mario once allegedly grabbed him on the street and tried to kiss him.
Representatives for both photographers said they were dismayed and surprised by the allegations. Tillman said Testino's brother came into the room and made the photographer get off Mr. Tillman. Another claimed Testino masturbated on him during a business trip.
Men said to the paper that they had asked to participate in "breathing exercises" which could include inappropriate touching, while model Bobby Roache said Weber tried to put his hands down Roache's pants during a casting in 2007.
Other men also told The Times that they have seen Testino fondle others or had fondled them on multiple occasions.
"We never had sex or anything, but a lot of things happened - a lot of touching, a lot of molestation". A lot of touching.
Another model described Testino as "a mentor who took it a step too far" after alleging he put his hands down his pants and turned up at his hotel room asking for sex.
Wood said he felt guilty because he knew he agreed to the impromptu session because "he was the photographer for Ralph Lauren".
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Model Monty Hooper said Weber told him he had "to learn to be more vulnerable" at a test shoot at the photographer's TriBeCa studio in 2014.
Many report being told to undress and take part in "breathing exercises" with Weber, while touching him and themselves.
"Like my agency said, he has a lot of power".
Lawyers acting for Testino, who is famous for his fashion portraits and photographs of the Royal Family, dismissed the models' accounts, while Weber's lawyers have also denied the claims, the paper said.
"We are deeply disturbed by these accusations and take this very seriously", reads the statement released by Anna Wintour, artistic director, and Robert A. Sauerberg Jr, chief executive. "[But] if you said you were not going to work with someone like Bruce Weber or Mario Testino, you might as well just pack it in and go work in another industry".
In her statement on the Vogue website, Wintour said: "Both (photographers) are personal friends of mine who have made extraordinary contributions to Vogue and many other titles at Conde Nast over the years, and both have issued objections or denials to what has emerged".
The new Code of Conduct includes only hiring models above the age of 18 and alcohol is no longer allowed on Condé Nast sets.
"Recreational drugs are not permitted", and any shoot involving nudity, skimpy clothing or sexual poses "must be approved in advance by the subject".