The forward had been traded to the Sharks by the Tampa Bay Lightning on Wednesday for forward Michael Eyssimont.
Namestnikov, who signed a one-year, $2.5 million contract with the Lightning on July 13, can become an unrestricted free agent after the season. The 30-year-old forward has 15 points (six goals, nine assists) in 57 games. He never played a game for the Sharks.
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Selected by Tampa Bay in the first round (No. 27) of the 2011 NHL Draft, Namestnikov has 251 points (113 goals, 138 assists) in 610 regular-season games with the Lightning, New York Rangers, Ottawa Senators, Colorado Avalanche, Detroit Red Wings and Dallas Stars. He has 11 points (six goals, five assists) in 48 Stanley Cup Playoff games.
Jets coach Rick Bowness was an assistant in Tampa Bay when Namestnikov first played there.
"It's a good addition," Bowness said. "'Vladdy,' first of all, he's a great person and great teammate. He's a very versatile forward who can play all three forward positions. He can kill penalties, you can throw him into the top-six every now and then, and if the power play is struggling, he can help that. It's his versatility that's the big attraction to him. Plus, he's a good teammate and a great person."
It's the second forward addition for the Jets, who acquired Nino Niederreiter in a trade with the Nashville Predators on Feb. 25. Niederreiter did not have a point in his Jets debut on Tuesday, a 6-5 shootout loss to the Los Angeles Kings.
"We added a top-six winger the other day, a guy that's scored 20-plus goals multiple times in his career, and I think that we added a player today that can play all over the lineup in a Vladdy Namestnikov -- can play center, can play wing," Jets general manager Kevin Cheveldayoff said. "I think those are things that we helped address. I think that we have depth in this organization with respect to defensemen, that we saved some room, that we can call up if we need to. We got opportunities to show that this group is the group that got us here and we have a lot of confidence in that it can take us to the next level."
The Jets (35-25-2) lost 6-3 at the Edmonton Oilers on Friday, their seventh defeat in eight games. They are fourth in the Central Division, one point behind the third-place Colorado Avalanche. They hold the second wild card into the Stanley Cup Playoffs in the Western Conference, five points ahead of the Calgary Flames.
The Sharks (18-32-12) are seventh in the Pacific Division and one point ahead of the Chicago Blackhawks for last place in the West.
NHL.com independent correspondent Darrin Bauming contributed to this report