The sale of the Brazilian is the latest in a string of high profile transfers involving foreign players and coaches in China, as its top league is increasingly flooded with cash.
But it is unusual for foreign stars to be traded between Chinese teams.
Evergrande are managed by former Brazil boss Luiz Felipe Scolari, while his longstanding rival ex-England boss Sven-Goran Eriksson coaches Shanghai SIPG.
“For the purpose of supporting Chinese teams to compete in the AFC Champions League, and for the national glory, we agreed Elkeson’s transfer,” the official news agency Xinhua cited Evergrande as saying in a statement.
The club, who won their second AFC Champions League title in three years in November, spent 5.7 million euros to bring the Brazilian to China in 2012, Xinhua said, and had recouped their investment many times over.
“Shanghai SIPG paid 18 to 20 million euros to the Guangzhou club,” it cited a source close to Elkeson as saying.
The 26-year-old scored 77 goals in three seasons for Evergrande, it added.
China’s most successful team, Evergrande this month raised $132 million from new investors in a deal that valued it at $2.4 billion — within striking distance of Manchester United.
Elkeson's Guangzhou record
- 2012 - Guangzhou Evergrande sign Elkeson for €5.7m
- Scores 77 goals in three seasons for Evergrande
- Wins three league titles (2013-15)
- Wins two Champions League trophies (2013, 2015)
But the club is far from profitable, losing $75 million in 2014, according to earlier results.
Wealthy businessmen have poured money into Chinese football clubs in recent years.
The investments come amid a state-led attempt to push the game with President Xi Jinping saying China hopes to host and even win a World Cup, ordering the game to be played more widely in schools.