The teenager teamed up with new squad Versa Motorsport for the shortened Australian Drivers' Championship season, the partnership yielding an impressive third in the standings behind Joey Mawson and James Golding.
That included three races wins and a lap record at the Hidden Valley circuit in Darwin.
Webster will continue driving for the team for the upcoming Tasman Series, which will take in the Gold Coast 500, the Bathurst International, and likely the Adelaide 500 as well.
"It's fantastic to be locked in for the Tasman Series this early so we can have the best possible preparation," said Webster.
"The progress we made as a team throughout the championship was incredible and at Darwin we really showcased what we are capable of.
"With a full year's worth of experience we are confident that we head to the Tasman Series as a contender for the championship, which will be out ultimate goal.
Versa team principal Toby Pope agreed that a Tasman Series title tilt is on the cards.
"We have always believed in Cooper's talent from the first time we saw him race, watching him beat current top level F2 and F3 drivers in his karting days," he said.
"Now it's been validated throughout the 2022 S5000 season for everyone else to see.
"At Cooper's age, with his talent, I don't think we'll be able to keep him for much longer so doing the best preparation possible to try and win the Tasman Series is the focus for the rest of 2022.
"This is the first of a number of announcements for the team moving forward as we count down to the streets of the Gold Coast in October."
The Tasman Series kicks off in Surfers Paradise on October 28-30.
