Liverpool are scheduled to hold a news conference later on Friday where they will unveil the 39-year-old former Swansea City boss as the man to revive the fortunes of the 18-times English champions.
While Swansea impressed in their debut Premier League season under Rodgers with an attractive, ball-retaining style, Liverpool supporters have voiced concerns whether he has the stature for one of England's most illustrious sides.
"I think they have made a very good appointment in Brendan Rodgers, I really do," Bellamy told reporters in Singapore on Friday as he unveiled the team's new kit for the coming season.
"He is very good guy as well, speaks well, knows his football, and he has proven himself."
"Liverpool is a huge, huge challenge. No disrespect to Swansea but this is Liverpool football club it certainly isn't Swansea," Bellamy, 32, warned Rodgers.
"So it is going to be a big test for him, but to me, if you know football, you know football, it doesn't matter what club you go to."
Rodgers also faces the tricky task of succeeding Kenny Dalglish, one of the club's most revered talents, having won league titles as a manger and player at Anfield.
He won praise for ending the club's six-year wait for a trophy when they won the League Cup in February, but sixth and then eighth place league finishes as great rivals Manchester United overtook them to win a record 19th title were heavily criticised.
"What he means to Liverpool Football Club is just indescribable and to be signed by him and to play for Liverpool Football Club under Kenny Dalglish was probably, truly, the greatest honour I
