Column Lodge, which was previously used as a register office was purchased by the Shropshire Bangladeshi Welfare Society from Shropshire Council.
Last month a man was cautioned in connection with comments he made on Facebook about the planned centre. Two other men were also arrested over the allegations.
Members of the English Defense League also staged two protests against the proposed centre.
A newly created anti-racism group called Hope Not Hate, this week showed support for the centre handing a petition into Shropshire Council with over 600 signatures.
Local residents showed concern over the lack of parking facilities at the building. It is understood that around 50 visitors would attend the prayer centre at peak times.
The prayer centre is expected to open later this summer.