Burns was a finalist for the Norris Trophy as the League's best defenseman last season, when he had 75 points (27 goals, 48 assists), all NHL career highs.
The Sharks lost a six-game series to the Pittsburgh Penguins in the Stanley Cup Final. Burns has 36 points (12 goals, 24 assists) in 58 playoff games.
"Brent is one the most dynamic players in the National Hockey League and we're very excited to get this deal done," Sharks general manager Doug Wilson said. "He has worked extremely hard to be an elite defenseman and at 6-foot-5, 230 pounds, his abilities on this ice are unique and rare. I also want to thank Hasso Plattner and our entire ownership group for their commitment to our franchise and the fans in San Jose by stepping forward and making this commitment to Brent."
Burns, who won the World Cup of Hockey 2016 and IIHF 2016 World Championship playing for Canada, has 16 points (seven goals, nine assists) in 19 games with the Sharks this season. He has 439 points (148 goals, 291 assists) in 816 games in 12-plus seasons with the Minnesota Wild and Sharks.
"This is a hard league, and every night it's tough and there are great teams," Burns said. "When you put yourself in the special group to fight for a chance, that's what it's about. We're trying to get back [to the Stanley Cup Final] and get over that next hurdle."