The Belgium international, 22, is set to move to the Premier League club in a £33m (40m euros) deal on Sunday.
Batshuayi, who scored 23 goals in all competitions for Marseille last season, will be new manager Antonio Conte's first signing at Stamford Bridge.
"This should be formalised tomorrow, I will leave Olympic Marseille this summer," Batshuayi wrote on Twitter.
Batshuayi came on as a substitute in Belgium's 3-1 Euro 2016 quarter-final defeat by Wales on Friday.
The Brussels-born forward, who signed for Marseille from Standard Liege in 2014, came off the bench to score in Belgium's 4-0 win win over Hungary in the last 16 on Monday.
He was linked with several Premier League clubs, and Crystal Palace reportedly agreed a fee with Ligue 1 side Marseille earlier this week.
Chelsea target Michy Batshuayi has confirmed that he will leave Ligue 1 side Marseille this summer.