Ivory Coast international Bony completed a move to the Liberty Stadium on Thursday in a club-record £12million transfer from Vitesse Arnhem.
He understands that it will take a big effort to succeed in English football but he hopes to match the achievements of his compatriot and fellow striker Drogba, who scored 100 goals in 226 Premier League games and won three titles for Chelsea.
Bony, 24, said: "Didier had a big career and scored a lot of goals in the Premier League, but I hope to do the same or more.
"I have spoken to him. He said congratulations and he is proud of me. He is a big inspiration for me. I have to listen to his advice and try to do what I can by giving my best.
"I will have to work hard because the Premier League is the next level up. He knows that if I believe then I can do well.
"Didier said Swansea was a good team who play very good football. There are not many teams in the UK who play like that.
"He said he knows how I play and I will enjoy playing for Swansea. He thinks I have made a good decision."
Bony insists he will not feel under any extra pressure after being bought for such a hefty fee, saying he is just delighted that a move was finally wrapped up.
He added: "It is a big transfer fee, but it is only a number. The most important thing is the team and the people involved in that.
"The transfer has been a long process, but I'm happy that everything is done now.
"I am now only thinking about the team and playing football.
"I have power and strength and I hope to bring what I know and do the most - score goals.
"I hope to replicate my form from last season and I think the style of football at Swansea will suit me."