Drogba, who didn't renew his contract with Chelsea has signed a two-and-a-half-year contract with the Chinese club.
Unconfirmed local reports said Shenhua are willing to offer the centre-forward as much as $15 million per year.
Bollywood actor Ranbir Kapoor said that Chelsea's iconic centre forward, Didier Drogba, is a legendary player.
Former Chelsea striker Didier Drogba said that the greatest achievement in his career was to win the Champions League trophy with the Blues last season.
Drogba also said that Lionel Messi is the best footballer he has ever played against.
Chinese clubs have been splashing out on big foreign managers and players to try to raise the profile of domestic soccer.
The Chelsea striker will play an exhibition football match on June 17 against a team including India's top cricketers.
The Chinese club is working round the clock to sign the striker following his departure from Chelsea.
The striker has insisted he will be determined to succeed next season following a "roller-coaster" campaign this year.
Didier Drogba believes Fernando Torres will key for the club next season following his own impending departure.
With the last kick in his last game, the 34-year-old Drogba won the Champions League for Chelsea in Munich.
Didier Drogba's Champions League-winning penalty kick was his last contribution to Chelsea as he has decided to leave the club after eight successful years.
Chelsea chief executive Ron Gourlay has also insisted that talks over the striker's future at the club are still ongoing.
Didier Drogba will visit India next month for the grand finale of the Pepsi T20 Football event.
Drogba has reportedly told his team-mates that "we will not be together next season".
Just one day after lifting the Champions League trophy, the Chelsea striker said he is not happy with his limited role on the team.
Drogba, who scored the decisive penalty to defeat Bayern Munich in the shoot-out of the Champions League final on Saturday, is out of contract next month.
In front of tens of thousands of Chelsea fans, the new kings of Europe paraded the Champions League trophy through London's New King's Road on Sunday.
The London club had been unable to win the Champions League until Di Matteo's brief - and officially temporary - tenure.
Lots of money, lots of luck and players who didn't care about winning ugly turned Chelsea into the champions of Europe.