The team announced the deal Friday. TSN reports it is worth $5 million.
"Dmitry is a young, talented and hardworking defenseman who continues to develop," general manager Dale Tallon said, according to the team's website. "He played well for our club last season and he will be counted upon to be an important part of our blue line this year."
The 22-year-old restricted free agent played for Yaroslavl Lokomotiv of the Kontinental Hockey League during the lockout, posting three goals and six points in 22 games.
Kulikov is entering his fourth NHL season having put up 13 goals and 70 points in 198 games for the Panthers, who made him the 14th pick in the 2009 NHL Draft.