The Welshman feels the former Swansea boss is a good choice but warns the incoming coach that he faces a big test of his credentials on Merseyside
Bellamy, who knows the the new boss well, feels the Northern Irishman is a "good appointment" for the Reds.
"I am sad to see Kenny go, but I think they have made a very good appointment in Brendan Rodgers, I really do," he told Sky Sports.
"I have got the chance to see him closely in the last few years because he is only down the road at Swansea and I am at Cardiff.
"He is a very good guy as well, speaks well, knows his football, and he has proven himself."
However, the former Wales international did acknowledge that Rodgers could face difficulties making the step up from the Swans to the Merseyside club.
"Liverpool is a huge, huge challenge," added Bellamy. "No disrespect to Swansea [but] this is Liverpool Football Club, it certainly isn't Swansea so it is going to be a big test for him."