"Chicago is a great place to be," Oduya said to TSN. "For me, I think it's really fun.
"Hopefully when you get brought somewhere they see that you can do some good for the team. That's what I want to come in and do."
Oduya, 30, has two goals and 11 assists with a minus-9 for the Jets in 63 games. He was a seventh-round pick of the Washington Capitals in 2001, and has played for New Jersey and Atlanta, moving with the franchise to Winnipeg this season.
He had a career-high seven goals and 22 assists in 2008-2009.
"His style really fits in with us," Chicago general manager Stan Bowman said. "He'll eat up minutes for us on defense."
Oduya will be an unrestricted free agent after this season, and his salary-cap hit will be $3.5 million.
Chicago, which has lost three straight, has been stretched thin on defense because of injuries to Steve Montador and Niklas Hjalmarsson. John Scott had been playing, but was ineffective in moving the puck.
"We knew we had to add experience on the back end," he said.
The Blackhawks ended up moving Scott to the New York Rangers before Monday's deadline, taking a 2012 fifth-round pick in return. Scott had one assist in 29 games for Chicago, with 48 penalty minutes.
The Blackhawks, 4-11-1 in their past 16 games, have gone from first in the NHL to sixth in the Western Conference in five weeks.
Oduya is expected to make his debut with the Blackhawks Wednesday night when they host Toronto.
Bowman said he talked with several teams, but couldn't make any other deals because the standings are so tight.
"More teams are in the mix (to make the playoffs), so there are not as many sellers," Bowman said. "We saw a lot of teams just pull back. We were open to anything."
Jesse Rogers covers the Blackhawks for ESPN 1000 and ESPNChicago.com. Information from ESPN.com's Pierre LeBrun and The Associated Press contributed to this story.