Drogba joined Wesley Sneijder at the club in the January transfer window, with Melo insisting that the pair's influence has helped the team.
"Their arrival has helped a lot. They are big names who have achieved so much, but there's nothing big-headed about them. They're prepared to dig in like anyone else, and that's been essential," Melo told FIFA.com.
"They had a big hand in us reaching the quarters and they've been crucial in the Turkish championship.
"Drogba is a role model. He won the Champions League for Chelsea, attracted big crowds wherever he went in China and he's got a lot of charisma in the dressing room. He's going to bring us trophies, and we're full of hope."
Galatasaray face Real Madrid in the first leg of their quarter-final clash in the Champions League on Wednesday.