Gala host Real needing to overturn a 3-0 deficit.
"I have a special relationship with the Champions League - it is a trophy I had to wait a long time to touch," Drogba told uefa.com.
"It is a real joy for me to be back in the Champions League, and especially to hear its anthem at the beginning of each game.
"I have found a club that is ambitious, with a great project. They at some point want to win the Champions League. It is a great choice for me.
"I wanted to rediscover the passion I experienced in Marseille. I want to be part of this adventure, part of this challenge. This is something very exciting."