The club issued a statement announcing the deal about 30 minutes prior to the NHL's collective bargaining agreement expiring at midnight Eastern time.
"Obviously very excited about it," Kane said on a conference call. "I'm grateful that the Winnipeg Jets took that leap of faith and make that kind of commitment."
Kane, 21, played in 74 games with the Jets last season, recording 57 points (30-27) and 53 penalty minutes.
He said he didn't feel pressure to get sign a new contract before the pending lockout.
"I think obviously you want to get a deal done as soon as possible, but things like this take time and it came up to the very last hour to get a deal done," he said. "Better late than never."
The Vancouver native has played in 213 career NHL games with Atlanta and Winnipeg, collecting 126 points (63-63) and 183 penalty minutes.
Kane, who was originally drafted fourth overall by Atlanta in 2009, said signing just before the lockout is a strange situation.
"You obviously want to play hockey," he said. "But at the same time I'm kind of on cloud nine and pretty excited about this contract."