The deal is worth $3 million total with a $1.5 million average cap hit, sources told ESPN.com's Pierre LeBrun.
The team announced the move Monday.
Miettinen appeared in 20 games with Ak-Bars Kazan of Russia's Kontinental Hockey League this season. He played with Minnesota during the 2010-11 season when he had 16 goals and 35 points in 73 games.
Miettinen has played in 472 NHL games overall with the Wild and Dallas Stars, recording 89 goals and 212 points.
Information from The Associated Press was used in this report.