Drogba, who scored the winning penalty in the Champions League final in May, signed a two-and-a-half-year deal with the Chinese club with his contract at Stamford Bridge set to expire at the end of June.
The Ivorian will link-up with ex-teammate Nicolas Anelka, who made the same move to China in January.
Drogba was an influential figure during his seven years at Chelsea and won the Premier League, the FA Cup and the Champions League with the west London side. Mata, who spent just one season with Drogba, used his Twitter account to send the 34-year-old his best wishes.
Mata wrote: "It's been a pleasure to play with you, thanks for everything you've given to us. Wish you the best!"
Mata, who also posted a photo of himself with Drogba, enjoyed Champions League glory in his debut season at Stamford Bridge thanks in no small part to the goals the striker scored on the way to the final.
Drogba grabbed crucial strikes against Barcelona and Napoli before equalizing against Bayern Munich and netting a famous spot-kick to guide the Blues to their first ever Champions League title.
Despite being linked with big money moves across Europe, Drogba decided to sign for the Shanghai club. He told reporters: "I considered all the offers I have received in the past few weeks, but feel Shanghai Shenhua is the right move for me at this time."
One of Drogba's first games for his new club will see him come up against familiar opponents when Manchester United play the Chinese side during their preseason tour of Asia.Follow GOAL.COM USA on