Drogba told Chelsea TV: "I am very happy to be here and am looking forward to playing for my new team.
"I want to do well with my national team and my club, so I will do my best to be better than I was last season at Marseille.''
The 26 year old will now jet out with the rest of the squad for our tour of the USA. But it is not yet known if he will be joined by Benfica midfielder Tiago. The Portugese international completed a medical at Stamford Bridge on Monday.
But there is thought to be a stumbling block with the deal, after Jose Mourinho announced "With Tiago, I don't know because I can't say he will be a Chelsea player.
"He is still a Benfica player. I understood some negotiations were made, but I am not sure about the end of them. So I don't want to talk about him.''
If Tiago signs before midnight on Tuesday, it will mean that Chelsea will have spent more money on transfers than any other British side in one day!