Proposed to be implemented in 2020, the council’s cabinet approved the submitting of the application to the Department for Transport which is now expected to be considered later this year.
Five "traffic wardens" have also been approved by the council as part of the civil parking enforcement instead of using an external company.
The officers will have a range of powers to deal with environmental crime and anti social behaviour, in addition to illegal parking.
West Mercia Police and Crime Commissioner John Campion has offered up to £200,000 to the council over a four-year period to support the implementation.
Councillor Richard Overton, Telford & Wrekin Council’s Cabinet Member for Enforcement said: "I want to stress that we will not be using an outside private firm for this enforcement role.
"By having an in-house team we can ensure they adopt an education-first culture, with enforcement as a last resort.
"We will definitely not be one of those councils chasing an income target and our officers will not be given targets to meet, unlike many other schemes across the country.
"This is not a money making scheme. If we were to be in a position where we have issued more parking fines than expected then any additional monies has to be spent on highway related improvements such as improving safer routes to school, improving off street parking and helping to maintain free car parking on many of our council owned car parks.
"We are often contacted by local residents on many occasions wanting us to tackle illegal parking in their locality and this leads to some frustration when we say we can’t take action as we don’t have the powers.
"I also believe that local residents appreciate that the police have greater priorities in tackling more serious crime than parking enforcement and are supportive of the council adopting these powers.”