The Wild received future considerations.
The 31-year-old defenseman had 24 points (seven goals, 17 assists) in 80 games last season and was plus-23, the best total of his 13-season NHL career. He also had one assist in two Stanley Cup Playoff games.
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Kulikov is entering the final season of a two-year, $4.5 million contract ($2.25 million average annual value) he signed with the Wild on July 28, 2021, and can become an unrestricted free agent after the season.
"This is a tough one, because he had a great year last year, played very well for us, but we need some more [NHL salary] cap space," Wild general manager Bill Guerin said. "We felt we had maybe one too many defensemen and we don't want to put guys in a position to where they're not playing or not playing enough. This has been talked about for quite a while with Anaheim, so it just kind of came to a head today, but we wish him nothing but the best."
Selected by the Florida Panthers in the first round (No. 14) of the 2009 NHL Draft, Kulikov has 198 points (42 goals, 156 assists) in 805 regular-season games with the Wild, New Jersey Devils, Edmonton Oilers, Winnipeg Jets, Buffalo Sabres and Panthers, and eight points (one goal, seven assists) in 29 playoff games.
The Ducks also signed defenseman John Klingberg to a one-year contract July 29.
NHL.com independent correspondent Jessi Pierce contributed to this report
