The 41-year-old right wing, who had surgery on his left knee in June, has spent 11 full seasons in Anaheim and helped them to their only Stanley Cup championship in 2007.
"I'm very happy that my knee has recovered from surgery and is ready for the season," Selanne said in a statement. "I'm excited and optimistic about what this team can do and thankful to have another opportunity to play in Anaheim."
Taken with the 10th overall pick in the 1988 draft by the Winnipeg Jets, Selanne recorded 31 goals and 49 assists in 73 games for the Ducks last season.
The Finn ranked third in the NHL with 16 power play goals and tied for eighth in overall scoring.
"As he showed again last season, Teemu still has the drive, determination, and skill to play at an elite level," Ducks general manager Bob Murray said in a statement.
"Most importantly for us, his passion comes from not just playing, but playing for the Ducks."
Selanne has represented Finland at five Winter Games, winning three medals, and is the all-time leading scorer in Olympic men's ice hockey with 37 points.
(Writing by Mark Lamport-Stokes in Los Angeles; Editing by Frank Pingue)