The 33-year-old arrived at Goodison Park earlier in the summer and is already eyeing up a regular place in the first-team.
Maarten Stekelenburg is hoping to make a strong impact at Everton
Stekelenburg arrived on Merseyside from Fulham last Friday and was put through his paces with his new teammates, including fellow keepers Robles and Mateusz Hewelt, earlier this week.
Following the departure of Tim Howard, the 33-year-old, who has spent the last two seasons out on loan at Monaco and Southampton, will fancy his chances of impressing new boss Ronald Koeman and establish himself as the first-choice option.
Having signed a three-year deal at Goodison, Stekelenburg says the move will bring some much needed stability to his career.
And the experienced shot-stopper, who has earned 54 caps for his country, says he cannot wait for the season to start.
He told the club's official site: “I want to play as much as possible and to give everything for the club and the fans.
“It’s nice to be staying longer than one year. The three-year deal is something I’m happy with. I’m looking forward to getting the season started.”
Stekelenburg's arrival has coincided with that of several familiar faces, including new goalkeeping coach Patrick Lodewijks, who has joined Koeman's new-look coaching team.
“He [Lodewijks] was the goalkeeper coach at Feyenoord," he added. "I’m from Ajax so there was a little bit of rivalry!
“He was also working with the national team and has a good reputation. I’ve met him a couple of times, he’s a nice guy and I’m looking forward to working with him.”
With Erwin Koeman also joining as assistant manager and Jan Kluitenburg appointed as fitness coach, there is a distinct Dutch feel to Everton's back-room setup, meaning it could provide the perfect environment for the new Toffees keeper to impress next season.