The Welshman feels the former Swansea boss is a good choice but warns the incoming manager that he faces a big test of his credentials on Merseyside
Rodgers has been unveiled as the new Reds boss, and Bellamy knows the 39-year-old well and stated he felt the Northern Irishman was a "good appointment" for the club.
"I am sad to see Kenny [Dalglish] 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 because he is only down the road at Swansea and I am at Cardiff so I have got the chance to see him very closely in the last few years.
"He is 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 Swansea City to the Merseyside club.
"Liverpool is a huge, huge challenge," added Bellamy. "No disrespect to Swansea this is Liverpool Football Club, it certainly isn't Swansea so it is going to be a big test for him."