Shropshire Council has sold Column Lodge to the Shropshire Bangladesh Welfare Society in a £215,000 deal.
The former church, based near to the Column roundabout, was home to the council's registration services before they were transferred to the Guildhall in Frankwell last year.
Martin Kabir, a trustee of the Shropshire Bangladesh Welfare Society, today said the building would become a Muslim prayer centre and community room, and it would be open to all members of the public.
He said: "The building was a place of worship years ago.
"It will become a facility for Muslim prayer and a day care centre. It is a first for Shrewsbury and everyone will be welcome.
"We have been looking for somewhere for a long time and this is close to the outskirts of town and easy to access."
A statement in support of the planning application said that at peak times on a Friday afternoon there could be up to 50 visitors.
But Mr Kabir said in general visitor numbers would fall. The building will be used as a place of worship between 4am and 11pm Monday to Sunday – with a maximum of 20 visitors expected per day.
The day care centre will be open between 4pm and 7pm from Monday to Friday, with a maximum of 10 children expected on site during these times.
One full-time caretaker will be employed to look after the building.
Steph Jackson, Shropshire Council's head of customer support and assets, said: "The council has agreed the sale of the building to the Shropshire Bangladesh Welfare Society, and as part of the sale process it has submitted an application to change its use.
"The sale will help the council to raise much-needed capital, plus save on day-to-day running costs."
People have until May 21 to comment on the proposals.