"After (Hulk) arriving in Shanghai, we will conduct a comprehensive medical check-up on him," Sui Guoyang, the Shanghai club's team manager, told reporters.
"We will sign the contract with him after we confirm all (health) details. Then we will have a media briefing."
The Brazilian international has scored 56 goals for Zenit in 97 Russian Premier League matches and was the league's top scorer in the 2014-15 season with 15 goals.
The Chinese Super League club are coached by the former England manager Sven-Goran Eriksson.
(Reporting by Nivedita Shankar in Bengaluru, editing by Ed Osmond)