Elkeson scored 59 times in 72 Chinese Super League appearances for Guangzhou, helping the club claim three successive domestic titles.
The 26-year-old was also key to their Champions League successes of 2013 and 2015, scoring the decisive goal in the final of the latter to secure a 1-0 aggregate victory over Al Ahli last November.
Guangzhou claim to have agreed the deal to benefit Chinese football as a whole with improved results in continental competition, but also acknowledged money was a motivating factor.
"For the purpose of supporting Chinese teams to compete in the AFC Champions League, and for the national glory, we agreed Elkeson's transfer to Shanghai SIPG," the club said in a statement carried by Xinhua news agency.
"The sale of Elkeson was for a record fee in the Chinese transfer market. The club got back its €5.7 million (£4.4m) investment and made a profit."
The 26-year-old was reportedly sold for €18m (£13.8m) and will now link up with former England coach Sven-Goran Eriksson.