"He told me yesterday that he made the decision by himself to stay for at least one more season," Koeman told the club's website after Everton's 2-1 victory over West Bromwich Albion on Saturday.
"It's great news for everybody."
Lukaku has scored 43 goals in 104 Everton appearances but had been linked with a return to Chelsea in recent months.
Koeman said there was also the possibility that the Belgian international could sign a new deal with the club.
Lukaku joined Everton on loan from Chelsea in September, 2013 before moving permanently in a club-record 28 million-pound deal a year later.
The striker moved to Stamford Bridge from Anderlecht in 2011 but failed to establish himself in London and moved on loan to West Bromwich 12 months after his arrival.
(Reporting by Ed Dove,; Editing by Ed Osmond)
