The Panthers' first-round pick in the 2009 draft, the 6-foot-1, 204-pound Kulikov has one year left on his contract and is set to make $4.5 million next season. He had one goal and 17 points in 73 games last year. Overall, Kulikov has 28 goals and 138 points in 460 career games.
The Sabres also got the No. 33 overall pick, which they used on Swedish two-way center Rasmus Asplund, who played on the same line as the Sabres' first-round pick, Alexander Nylander, at the world junior championships.
Sabres GM Tim Murray was vocal about his desire to acquire a left-handed, top-four defenseman and was believed to be talking to the Anaheim Ducks about Cam Fowler. But his focus then turned to Kulikov, who became expendable when the Panthers signed Keith Yandle to a six-year deal earlier this week.
Pysyk, the Sabres' 2010 first-round pick, had difficulty establishing a regular role in Buffalo. He has split each of the past four seasons between Buffalo and its American Hockey League affiliate in Rochester.
The Associated Press contributed to this report.