The Ivorian joined Chelsea in 2004 for £24million and helped his side to six trophies during Mourinho's first tenure at Stamford Bridge.
The Galatasaray striker is set for an emotional return to Stamford Bridge after the Turkish side drew Chelsea in the last 16 of the UEFA Champions League, with Drogba reserving special praise for his former boss.
"When Chelsea were thinking of signing me, it was Mourinho who came to see me," he told the Sun.
"He said 'If you want to be a great forward like Thierry Henry or Ruud van Nistelrooy, you have to come and play with me in England, at Chelsea'.
"It's true that I was a good player in the French league at the time but he made me one of the best in Europe.
"That's why I, for Jose, was capable of going to the ends of the earth."
Drogba says that Mourinho, who returned to Stamford Bridge in the summer after a six-year absence, revolutionised the Blues by instilling a winning mentality throughout the squad.
"Before Jose arrived Chelsea had good players. John Terry and Frank Lampard were quality players," added Drogba.
"When I arrived I already knew how to play football. Petr Cech also knew how to play football. But Jose transformed good players into winning players. We only thought about winning.
"He adores winning. The majority of coaches arrive at a club and say 'I'll try to win but it'll be difficult'. He says 'I'm here to win' and he wins. That makes him special.
"Even after Mourinho left, that winning mentality stayed there. He left that legacy at Chelsea."