Nine-times grand prix winner Webber started working with Piastri in 2019 and was instrumental in the driver joining McLaren in 2023 in place of compatriot Daniel Ricciardo and instead of remaining with Alpine.
Renault-owned Alpine had wanted to promote Piastri to a race seat after double world champion Fernando Alonso announced he was leaving for Aston Martin, but the Australian rejected the offer.
"We are proud to have played a pivotal role in the formative years of Oscar's career and to have placed him in F1 so that he could compete at the front so early in," Webber said in a statement.
"Following our reduced trackside involvement this season, we have collectively agreed that now is an appropriate time to bring our management agreement to a close.
"This will allow Oscar to build on his achievements under a new management structure and for us to embark on our new ventures."
Piastri, who won back to back titles in Formula 3 and Formula 2 in 2020 and 2021, thanked the pair for support and recognised their guidance had been invaluable.
The Australian has not won a race this season, after looking like he might win the championship last year before being overhauled by teammate Lando Norris and ending up third. He finished sixth in Brazil on Sunday.
The winner of nine grands prix has not been on the podium for 16 races and is lying seventh in this year's standings.
