The deal is worth $18 million, a source told ESPN.com. The $4.5 million average salary is well above the $1.3 million Hiller is earning this year.
The 27-year-old Hiller, who will start in goal for Switzerland next month at the Vancouver Olympics, was slated to become an unrestricted free agent July 1.
"This is a very exciting day for me personally," Hiller said. "Anaheim has been a great place to play, and I couldn't be happier to stay here."
Hiller is 21-15-2 this season with a 2.75 goals-against average and .916 save percentage. Last spring in the Stanley Cup playoffs, Hiller went 7-6 with a 2.23 GAA and .943 save percentage as the Ducks upset top-seeded San Jose in the first round and pushed eventual Cup finalist Detroit to seven games in the second round.
"Jonas has proved himself as a starting NHL goaltender," general manager Bob Murray said. "We expect him to only get better."
Hiller has a 54-37-4 career record with a 2.46 GAA and .919 save percentage. That save percentage is the third-best in the NHL in that time period, behind only Tim Thomas and Tomas Vokoun. Hiller was signed as a free agent by the Ducks from Europe in May 2007.
Pierre LeBrun covers the NHL for ESPN.com. Information from The Associated Press was used in this report.