Thomas Greiss has proved that his superb 2015-16 season was no accident. Now he has the contract security to back that up.

The Islanders signed Greiss to a three-year, $10-million extension Monday night, ensuring that the 31-year-old goalie will be part of a more stable situation in net.

“It’s the most success I’ve ever had playing hockey, so it’s been fun,” Greiss told Newsday after signing his deal. “It’s a great organization; we have great guys on the team. That makes you more comfortable on the ice, too.”

Greiss bounced between the Sharks, Coyotes and Penguins in his first six seasons, making 69 starts, before signing a two-year, $3-million deal on July 1, 2015, to be Jaroslav Halak’s backup.

Greiss was the opening night starter when the Islanders made their Barclays Center debut in October 2015, and last spring, he backstopped the Islanders’ first playoff series win since 1993. He’ll make his 62nd Islanders start Tuesday night against the Capitals, having recaptured the No. 1 job after the Isles sent Halak to the AHL on Dec. 31.

Greiss is third in the NHL with a .937 even-strength save percentage and recently posted a 154:10 shutout streak.

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It’s been a long road for Greiss, who was a third-round pick of the Sharks in 2004.

“Everyone has some self-doubt along the way, but if you don’t have confidence, you don’t get far in this league,” he said. “You always believe in yourself, try to have fun, play your best and see where it gets you.”

Greiss will be the one goaltender the Islanders protect in the June expansion draft. Halak still has one year left on his deal and J-F Berube, Greiss’ backup, still is a candidate for the No. 2 job next season.

The Islanders kept all three goaltenders active through the first three months of the season, but Greiss isn’t concerned about it happening again.

“I’m not too worried about it,” he said. “It’ll work itself out. I’m more concerned with us trying to make the playoffs right now.”

Notes & quotes: The Isles returned from the All-Star break without three injured regulars. Travis Hamonic (knee) remained out, as he’s been since Jan. 8. Thomas Hickey (lower body) and Cal Clutterbuck (lower body) also missed practice, and Doug Weight ruled both out for Tuesday night. John Tavares missed practice after taking a red-eye flight from Los Angeles but will be in the lineup.