Piastri has signed with Jam Sports Management, a sports agency founded by Webber and his wife Ann.
The 18-year-old will race for Prema in F3 this year, the team that dominated the teams' championship in 2019, winning eight out of the 16 races in the series, finishing 304 points ahead of second-placed Hitech Grand Prix.
In January, it was announced that Piastri had joined the Renault Sport Academy. In 2019, he won the Formula Renault Eurocup.
“Oscar is an impressive young man,” Webber said. “I’ve enjoyed watching him continue his education and do the normal things kids his age do while dovetailing it with his racing – the level of self-discipline and dedication he has shown is admirable.
“What Oscar managed to do last year in Formula Renault was also pretty special, how he took control of the championship and closed the title out.
“He’s got that white line fever when he puts his helmet on and turns into a different character, which is sensational.
“Oscar is in a great position with Renault, they are investing in him, they believe he’s a horse worth backing and keeping a tight eye on, and that’s exciting for him and Australian motorsport.
“He’s trying to get to an extremely tough category in Formula 1, and he knows what’s ahead of him, but Renault and ourselves know Oscar is an incredibly confident young lad, and we think he can do great things.”
Piastri added: “I’m excited to start working with Mark and Ann; I think everyone in Australia knows who Mark Webber is and he’s a pretty big name to have on my side.
“Mark’s been through Formula 1, LMP1, and other categories through the years, so he has the experience that I’m sure if I have any issues, he will be able to steer me in the right direction or to the right people in the paddock.
“It doesn’t change how I go racing; my goals are still the same; it’s just that I’ve got outstanding people in my corner now.”
Bahrain International Circuit - Winter testing