Seven of the eight current town councillors will return to their roles, including mayor Grant Perry.
Julie Magill will step down and will be replaced by newcomer Tim Halford.
The council has 12 seats but has struggled to fill them in recent years.
The four vacancies will be filled by co-option or by-elections at a later date.
With all candidates elected unopposed, there is no need for an election to be held on May 6 as planned.
Voters in the town will however get to cast their ballots in the Shropshire Council and West Mercia Police and Crime Commissioner elections on the same day.
Town and unitary councillor Ruth Houghton will defend her Shropshire Council seat for the Liberal Democrats, going head to head with current Much Wenlock councillor David Turner for the Conservatives, and Green candidate Linda Senior.