St Helens claimed five premierships during Mike Rush's leadership, including four consecutive grand final wins from 2019 to 2022.
The club also defeated Penrith in the 2023 World Club Challenge.
Rush left the St Helens chief executive role in February after 13 years in the position and 27 seasons with the club.
He has replaced Jim Sarantinos at Parramatta, where the Eels have not won a premiership since 1986.
In his first interview since his appointment, Rush said the club did not need a rebuild.
He said he would provide coach Jason Ryles, whom he had once tried to recruit, with a competitive roster and make the Eels "competitive, quickly".
Rush also said he would make the difficult decisions needed to bring success to Parramatta.