Tampa Bay signed the 31-year-old free agent to a two-year, $3 million deal Monday, but had to wait for Miettinen to clear waivers.
Miettinen began the season in Russia's KHL with the Kazan Ak-Bars, registering two goals and six assists in 20 games. He played with Minnesota during the 2010-11 season, when he had 16 goals and 35 points in 73 games.
Miettinen has appeared in 472 career NHL games with the Dallas Stars and Wild, recording 89 goals and 212 points.
The Jets also activated defenseman Ron Hainsey from injured reserve.