The Cote d'Ivoire international is determined to give his best for his new club and has admitted his decision to move to Turkey was influenced by his former Chelsea boss
The ex-Chelsea star this week indicated he was delighted to have returned to Europe with the Istanbul-based club after his brief and unhappy spell in China.
At Galatasaray, Drogba will link up with national team-mate Emmanuel Eboue, who he said he also went to advice for along with Mourinho before his move.
"Before signing, I talked with Eboue a lot. I talked with Mourinho and some other guys," Drogba told Galatasaray TV.
"Everybody said that Galatasaray is a very big, passionate and unique club.
"Being at Galatasaray with [Wesley] Sneijder means a message to Europe's big teams. I want to win Champions League again. We'll do our best [in our last 16 clash] against Schalke."
"I'm fit now and I will be ready to play in a very short time."
The Ivorian explained the reasons why he elected to wear the No.12 shirt while thanking his new fans who came in droves to witness his arrival.
"I choose No.12 because No.11 is in use and No.12 reminds me of my daughter's birth date," he added.
"The fans were amazing when we arrived at the airport. I thank them all."
Gala coach Fatih Terim is delighted at the arrival of the Champions League winner and is sure he will improve his side.
"I'm very happy at signing a player of Drogba's quality," Terim said.
"He is a very important striker. We have a strong squad and Drogba will make it stronger."