The Italian international will make his Anfield debut on Saturday against Aston Villa and is in line to lead Liverpool's attack with Daniel Sturridge ruled out with a thigh strain.
Hamann stressed how important it is for the mercurial forward to show he has matured in order to flourish but believes Liverpool have got a bargain if he can do so.
"He has still got to prove he is a team player because where he has been in the past he has caused trouble more often than not," Hamann said.
"He had a very encouraging start at Spurs. Hopefully he carries on in that vein.
"There is no doubt he is a fantastic talent. For £16m, you have got to say he is a bargain."
Former Liverpool midfielder Jason McAteer is confident that the club have the characters in the dressing room to keep Balotelli in line if he begins to cause trouble.
"You've got to let Mario be himself," McAteer said. "When he steps over the line, that is when you have a word with him.
"There are big players in that dressing room - big voices, big men - and they will pull him to one side as soon as he steps out of line.
"But until he does I'm going to give him the benefit of the doubt. He has done nothing wrong up to now."
Jan Molby is confident the striker can regain his best form under Brendan Rodgers and is hopeful he will stay at the club for years to come.
"I see the talent like everybody else," Molby said. "How long we can keep him motivated for is obviously the key.
"He did very well in his first game. I think it's going to be a special occasion for him playing at Anfield.
"The talent is there, the boy is capable of doing anything but I just hope he has now found his home and he goes 'this is where I want to do my stuff'."