The 25-year-old Brazil international said earlier this month the transfer was "90% certain".
Oscar joined Chelsea from Internacional for £25m in 2012 and has scored 38 times in 203 appearances for the club.
He will complete his move "at the beginning of the January transfer window", the club said in a statement.
Oscar, who has struggled to get into Antonio Conte's Chelsea side since October, will join former Blues boss Andre Villas-Boas in Shanghai.
The Chinese side confirmed Oscar "will arrive in Shanghai in the coming days to officially join SIPG".
The player, who has won the Premier League, Europa League and League Cup during his four-and-a-half-year spell at Stamford Bridge, will earn a reported £400,000 a week and the transfer fee will rank as the seventh-highest of all time.
Conte last week said the huge money being spent on players by Chinese clubs was a "danger for all teams in the world".
Oscar's move comes as former Manchester City forward Carlos Tevez is reportedly on the verge of becoming the world's highest-paid footballer by moving from Boca Juniors to Shanghai Shenhua, where he will earn £615,000 a week.
The transfer window opens on 1 January and closes at 23:00 GMT on 31 January.
Chelsea and Shanghai SIPG have agreed terms for midfielder Oscar's estimated £60m move to the Chinese Super League club in the January transfer window.