The former Blackhawks center is now headed to Carolina.
The forward's deal carries an average annual value of $6.25 million and runs through the 2021-22 season.
Joe Thornton – the second leading scorer in San Jose Sharks history – re-signed on Sunday in a one-year deal reportedly worth $6.5m.
Evgeny Kuznetsov is staying with the Washington Capitals, signing an eight-year contract.
The Caps locked up the 25-year-old center with an eight-year deal worth $62.4 million.
The Toronto Maple Leafs have signed veteran forward Patrick Marleau on a three-year deal.
Mr. Shark is now Mr. Leaf.
Schultz had a plus-27 rating this season, sixth among NHL defensemen, and two winning goals and seven power-play points in the playoffs.
Thornton is the second-leading scorer in Sharks history with 937 career points.
Kevin Shattenkirk reportedly turned down "far more money on longer-term deals" to sign with the Rangers.