The council says the move is necessary to reduce the amount of cash it has to deal with, and to give motorists more choice over how they pay to park.
Currently, people parking up in the town council-owned Central, Smithfield Street and Horsemarket car parks can only pay by cash or through MiPermit.
The installation of the new contactless machines was agreed at a meeting on Monday evening, but members stressed that cash will still be an option for people who want to pay that way.
Operations manager Henry Teuma told councillors all machines needed to be upgraded to make them 4G compatible, which presented the opportunity to include a contactless card payment option.
He said: “Shropshire Council do use a lot of card payments and the data I have received from them is that 60 per cent of transactions are either online or by card.”
Mr Teuma said contactless payments would incur a fee, costing the council around 18p per transaction.
By comparison, payments made through the MiPermit app incur a fee of 10p.
Councillor Mike Isherwood criticised the transaction fees but accepted: “This is something that does need to be done. I think we want to push the MiPermit system a lot more as the transaction fees are less.”
Councillor Les Maguire said it was important to highlight to residents that cash payments will still be accepted at all machines.
A report to members said upgrading all 15 machines across the three car parks to 4G would cost £7,016 plus VAT, and including the contactless payment option would bring the total to £21,269 plus VAT.
Mr Teuma instead recommended including contactless payments on just one machine per car park. This option would cost £9,668 plus VAT.
However Councillor Olly Rose suggested Central Car Park should have two machines due to its size.
Councillors unanimously agreed to the changes.