Koeman brought in experienced the Dutch goalkeeper as his first signing at Goodison Park.
Everton manager Ronald Koeman has explained, as quoted by the Liverpool Echo, that he signed experienced goalkeeper Maarten Stekelenburg to compete with Joel Robles and claimed that the Dutch stopper's best years are still ahead of him,
Koeman made Stekelenburg his first signing since taking over from Roberto Martinez as Toffees manager when he brought the 33-year-old in from Fulham earlier this month.
Stekelenburg played under Koeman at Southampton last season during a loan spell, and the Dutch boss clearly saw enough from the player to be convinced that he would be a good addition to his squad at Goodison Park.
Following the departure of long-serving veteran Tim Howard to Colorado Rapids, last season's first choice Joel Robles was left as the club's only senior goalkeeper, and strengthening the options in that position was a summer priority.
Despite Stekelenburg's advancing years, Koeman believes that the signign made perfect sense for Everton as he says the best part of the former Netherlands number one's career is still to come.
Koeman said, as quoted by the Liverpool Echo: "I'm very pleased, you know we had Joel (Robles) as the goalkeeper and we need competition in that position.
"I know Maarten very well. I took him to Southampton and he did a good job. First of all he brings quality which is very important and then he's a goalkeeper with experience.
"Six summers ago he played in the final of the World Cup in South African in 2010. Goalkeepers have their best seasons from the age of 30. He's 33 and still has a good future as a goalkeeper ahead of him and that's very important."
Stekelenburg, who won 54 caps for the Netherlands between 2004 and 2012, will now compete with Robles for the number one spot at Goodison Park under Koeman.