"They were a team that was interested throughout the process," Nyquist said. "It was a pretty stressful process. There were a lot of decisions to be made pretty fast, on pretty short notice."
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The 29-year-old forward had an NHL career-high 60 points (22 goals, 38 assists) in 81 games with the San Jose Sharks and Detroit Red Wings last season, including 11 points (six goals, five assists) in 19 games after he was traded to San Jose on Feb. 25.
Nyquist had 11 points (one goal, 10 assists) in 20 Stanley Cup Playoff games.
Columbus defeated the Presidents' Trophy-winning Tampa Bay Lightning in the Eastern Conference First Round to win a playoff series for the first time.
"It's a team that had a really good season, some really good young pieces and also some veteran leaders and a team that's really heading in the right direction," Nyquist said. "You saw that in last year's playoffs. Those were things that really excited me."
The Blue Jackets lost left wing Artemi Panarin, who signed a seven-year, $81.5 million contract as a free agent with the New York Rangers. Panarin led Columbus with 87 points (28 goals, 59 assists) last season.
"Now that we've added Gustav Nyquist, we filled a hole that was created on the left side," general manager Jarmo Kekalainen said.
Center Matt Duchene (Nashville Predators) and goalie Sergei Bobrovsky (Florida Panthers) also left the Blue Jackets as free agents.
Selected by Detroit in the fourth round (No. 121) of the 2008 NHL Draft, Nyquist has 306 points (131 goals, 175 assists) in 500 games with the Sharks and Red Wings, and 19 points (five goals, 14 assists) in 55 NHL playoff games.
"Gustav Nyquist is a skilled, fast, two-way player who will be a great addition to our club both on the ice and in the dressing room," Kekalainen said. "He is a talented playmaker with a versatile game who has been extremely durable throughout his career, and we are very excited to welcome him to the Blue Jackets family."
NHL.com correspondent Craig Merz contributed to this report