The 31-year-old had moved to San Siro in 2016 after a fruitful spell with Sampdoria, but managed only 14 goals in 86 appearances for the Nerazzurri.
Jiangsu are owned by Suning, the same organisation that is now a majority shareholder in Inter.
Jiangsu finished 12th in last year's Chinese Super League, but have improved to fourth in the current campaign.
He made his Italy debut in 2015 during his time at Sampdoria and has gone on to play 26 times for his country. Having scored twice in the qualifying campaign for Euro 2016, Eder made the final squad and scored the only goal in the 1-0 win over Sweden in the group stage.
He scored three goals in six internationals in 2017, but could not help Italy reach the 2018 World Cup, with the Azzuri finishing second in their group behind Spain before being knocked out by Sweden in the play-offs.
As well as new Jiangsu team-mate Gabriel Paletta and former Southampton striker Graziano Pelle of Shangdong, Eder will be one of three Italy internationals in the Chinese Super League this season.