Reports had suggested that the 23-year-old was set to leave Goodison Park, with Chelsea said to be interested in signing the Belgium international.
"It's great news for everybody," said Koeman after the 2-1 win at West Brom, during which Lukaku came on as a first-half substitute.
Asked if he might be offered a new deal, Koeman said: "That's possible."
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Lukaku spent a season on loan at Everton in the 2013-14 season, scoring 16 goals, before he made the permanent move from Chelsea for a club record fee of £28m.
He scored 20 times for the Toffees during the 2014-15 campaign and found the net on 25 occasions last season.
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Everton striker Romelu Lukaku will stay at the club for "at least one more season", says manager Ronald Koeman.