Tevez, 32, has long been expected to complete the switch, which was confirmed by both clubs.
The Argentine is reportedly becoming the highest-paid player in the world with his move to the Chinese Super League (CSL).
In a statement, Boca wished Tevez – who returned to his boyhood club last year and won two more trophies – all the best.
“Good luck Carlitos,” a statement read. “You will always be in our hearts.”
Tevez’s arrival is a boost to Shenhua, who finished fourth in the CSL in the 2016 season.
He joins the likes of Demba Ba and Obafemi Martins in Gus Poyet’s squad.