"It is not going to be easy because Pirates have good strikers, but I will do my best," Mbesuma told the City Press.
"It means there is something special about me. But that does not mean I have to relax. I still have to prove myself.
"I want to be successful with Pirates and win things with them. I think I need competition and I know Pirates is a big team so I just want to compete," he added.
Pirates coach Augusto Palacios said the Zambian striker was the last signing for the season.
"Collins is the last player coming to Pirates to strengthen the squad for the PSL and Africa campaigns. We take this very seriously," said Palacios.
Mbesuma has played for Kaizer Chiefs, Mamelodi Sundowns and Moroka Swallows.
Mbesuma made his debut for Zambia in 2003.
Kaizer Chiefs bought him in January 2004 from Roan United in Zambia.
Mbesuma was named PSL Player of the Season in 2005 after scoring 35 goals in one season with Kaizer Chiefs.
He then caught the attention of Bolton Wanderers and Portsmouth but he failed to secure a deal with the English clubs.