Argentine media previously reported Tevez would make $84 million over two years under the contract.
The acquisition of the 32-year-old from Buenos Aires side Boca Juniors will "greatly enhance" the team's front line, Shenhua said on a verified social media account.
"The club looks forward to Tevez helping Greenland Shenhua attack cities and strike stockades in Asian and domestic matches and contribute to more exciting games for fans," it said, calling him "the most outstanding striker in Argentina's history".
It did not put a value on the transaction, but Argentine media previously reported Tevez would make $84 million over two years under the contract -- 20 times his previous earnings.
In a statement Boca thanked Tevez, who was on his second spell with the club, scoring 25 goals in 56 matches, including a double in a 4-2 Clasico victory over their bitter rivals River Plate earlier this month
Boca wished him good luck, saying he had left fans with "unforgettable memories" and telling him they would be "dreaming of your return".
"We'll work on bringing you back," it added. "No effort is too great to have you wearing our shirt again."
After passing a medical Tevez will join the rest of the squad on the Japanese island of Okinawa, where they are holding pre-season training until late January, according to Shenhua.
The side are coached by former Uruguay international Gus Poyet, who was installed last month after the club parted ways with his Spanish predecessor Gregorio Manzano despite finishing fourth in the Chinese Super League.
If reports are correct, Tevez's $42 million annual salary would make him the world's best-paid footballer in terms of earnings from his club, catapulting him past the previous top three: Cristiano Ronaldo, said to take home $23 million a year after tax from Real Madrid, his teammate Gareth Bale, and FC Barcelona's Lionel Messi.
All top footballers pad their salaries with lucrative sponsorships, which can send their incomes even further into the stratosphere.
Tevez is the latest international name, many of them South American, lured to Chinese football for eye-watering sums of money.
Crosstown rivals Shanghai SIPG, coached by former Tottenham Hotspur manager Andre Villas-Boas, last week agreed a reported £60 million deal ($73 million, 70.5 million euros) for Chelsea's 25-year-old Brazilian midfielder Oscar.
Before the Oscar deal Chinese Super League clubs had already splashed out more than $400 million on players this year, after President Xi Jinping laid out a vision of turning the country into a football power.
Chinese teams broke the Asian record three times in just 10 days in the January-February transfer window, and moved it still higher when Brazil's Hulk joined SIPG for 55.8 million euros in July.
Significantly, Chinese clubs are now competing with European rivals for world-class players, who are opting for astronomical pay packets over the chance of a career in football's top leagues.
Fans welcomed the latest deal. "Shanghai’s football has had its spring," said one poster on China's Twitter-like Weibo. "Aren't you looking forward to next season's Shanghai derby?"
Tevez, who has also played for Italian side Juventus during his career, has more than 70 caps for Argentina. He married the mother of his three children, Vanesa Mansilla, last week in Uruguay only to discover that his home had been burgled when he returned after the ceremony.