The Victorian Society, which originally had opposed the plans, now supports the trust's decision after visiting the site in January.
Ian Dungavell, director of the society, told the BBC that he was keen to protect the hospital's Grade II Victorian buildings, designed by prison architect Joshua Jebb.
Last month after the plans were given council approval, Vickie Holcroft, programme director for the Broadmoor redevelopment, said officials were delighted.
"We're delighted with the Council's decision to give this extremely important project the go ahead," she said.
"I hope the council's backing goes some way in helping the Trust achieve its goals and continuing with the often difficult, but necessary work of rehabilitation of these severely, mentally ill patients."
In 2003 the ageing Victorian buildings were declared "unfit for purpose" by the Commission For Healthcare Improvement.
Some of the country's most notorious killers and sex offenders have been treated within the hospital. The Yorkshire Ripper Peter Sutcliffe is detained at Broadmoor.
The trust said it was "confident" a buyer could be found.