Telford & Wrekin Council said the increase would help to offset cuts in Government grants for social care.
The increase is equivalent to an extra 60p a week for the average borough Band B home.
Councillor Lee Carter, cabinet member for Finance, said that, despite the cuts, the town would still have one of the lowest council tax rates in the Midlands.
"Last year many councils with social services responsibilities raised council tax by almost six per cent," Councillor Carter said.
"We have instead chosen more gradual increases of 3.2 per cent in 2018 and 2019 but make no mistake we are very aware of the impact that this huge bill has on households in the borough."