Brick was appointed to the role on an interim basis in January following the departure of Philip Mountford. He joined as non-executive director in September.
Moss Bros chairman David Adams said: "Brian is the right person to lead the company through what will be an extremely challenging period for the retail sector.
"He has a proven track record in the menswear sector and has the experience together with the senior management team to guide the company through the current recession and ensure the company maintains its position as the UK's No. 1 branded suit specialist."
Brick was formerly managing director of Speciality Retail Group, which he sold in 2005.
Meanwhile, it is understood thatSpeciality Retail Group is restructuring to combine functions with BMB Group as it counters the effects of the downturn.
Speciality Retail Group is owned by Egyptian supplier Arafa Holdings is believed to be merging some of its functions with BMB, in which Arafa has a majorty stake.
Speciality Retail Group's buying and merchandising funcations for Suits You and Racing Green will relocate from Borehamwood in Hertfordshire to Leeds, where BMB is based.