According to TSN, the deal is worth an average of $4.33 million per season.
In other moves, the Jets signed goalie Steve Mason to a two-year, $8.2 million deal -- with an average cap hit of $4.1 million -- and agree to terms with forward Michael Sgarbossa on a one-year, one-way contract for $650,000
At only 26, Kulikov is one of the youngest unrestricted free agents on the market. His name was bandied about quite a bit at last season's trade deadline since Buffalo had fallen out of contention, but he was not moved by the Sabres.
Kulikov had a down year last season after a trade from Florida to Buffalo. He had only five points and was a minus-26, but he battled a back injury much of the season and played in only 47 games.
The third and final year of the contract he signed with Florida had a cap hit of $4.33 million.
The 29-year-old Mason battled a hand injury early in the season and lost his No. 1 spot to Michal Neuvirth with the Flyers. Toward the end of the season, he regained the starting position, however, and went 10-5-2 with a 2.14 goals-against average and .926 save percentage over his last 17 games.
At the end of the season, Mason said he did not want to split time in the future and considered himself a clear No. 1. Neuvirth shockingly collapsed on the ice in April and doctors never found the exact cause, but he was cleared to return and signed an extension with the Flyers in March.
Sgarbossa, 24, split last season between the Ducks and Panthers, finishing the season with two goals and seven assists in 38 total games.