Speaking at CAA's World Congress of Sports conference in Los Angeles, Eghbali gave his most direct statement of support for the head coach since a downturn in form began following a 5-2 defeat at Paris Saint-Germain in March.
"On Liam, we had the opportunity to work with him daily for 18 plus months, so we knew what we were getting. We think he has every attribute to be successful here."
"He got off to a great start. We've had a tough past five, six matches, but I think we're behind Liam. Of course, it's a results business, but we think he can be successful long term."
Rosenior was appointed in January after the surprise sacking of Enzo Maresca on New Year's Day. Eghbali acknowledged that decision was not straightforward, describing it as "not a change we wanted to make." The 41-year-old had previously managed BlueCo's sister club Strasbourg and signed a contract with Chelsea running until 2032.
In 21 matches, Rosenior has won 11, lost eight and drawn two. Chelsea are sixth in the Premier League after 32 games, four points outside the top five, with Champions League qualification far from assured.
Eghbali also addressed the club's transfer approach, promising a shift towards more experienced signings after seasons dominated by young talent. "The view is now that we're here with a great core base, to add some of that experience, to take the team to the next level and have consistency," he said.
Fan protests against the ownership group are planned ahead of Saturday's home match against Manchester United, with the Chelsea Supporters Trust having also issued an open letter expressing a lack of confidence in the board's direction.