The 23-year-old forward, who was a restricted free agent, led the Stars in goals (41), power-play goals (13), shots on goal (220) and shooting percentage (18.6 percent), and was second with 79 points (41 goals, 38 assists) behind Joe Pavelski (81 points) in 74 games last season. He had four points (one goal, three assists) in seven Stanley Cup Playoff games.
Robertson had not been with the Stars during training camp. Dallas plays its preseason finale Saturday at the Minnesota Wild before its season opener Oct. 13 at the Nashville Predators.
"I think the first thing was obviously relief," he said Thursday. "You never really want to stay out this long, especially with the season starting in a week from today. Things kind of gained momentum yesterday. (Agent) Pat (Brisson) told me that stuff was happening, and eventually we made that decision and it was definitely a relief. … I think it was 1 in the morning (ET) when it happened, so there wasn't much energy, but definitely had a little jitters going that the season is going to start soon and I'm going to be part of it.
"I have about a week, probably four or five practices with the team to get accustomed. I'm in good shape. I feel good, as far as conditioning I feel great. All the mental on-ice stuff and everything else, we'll see what happens over the next couple of days."
Video: Jason Robertson\ comes in at number 37 on the Top 50
Robertson was the runner-up to Wild forward Kirill Kaprizov in voting for the Calder Trophy, awarded to the NHL rookie of the year, in 2020-21 when he had 45 points (17 goals, 28 assists) in 51 games. He will play for a different coach this season; Peter DeBoer was hired June 21 to replace Rick Bowness, who resigned May 20 after three seasons.
"I know there's a whole coaching staff and everything's new there," Robertson said. "I think I'm a great learner, and a fast learner at that too. I don't think it'll take me too long to get adjusted, but that's part of being a professional hockey player, to adjust."
Selected by the Stars in the second round (No. 39) of the 2017 NHL Draft, Robertson has 125 points (58 goals, 67 assists) in 128 games.
"Jason is an integral part of the present and future of our team and we're thrilled to have him for the next four years," general manager Jim Nill said. "Since he was drafted by our organization, he has worked tirelessly to become a better player every day. His knack for scoring goals and seeing plays develop on the ice are just some of the tremendous assets that he brings to our team. He is one of the best young players in the NHL and we look forward to seeing him continue to progress."
Goalie Jake Oettinger, who was a restricted free agent, signed a three-year, $12 million contract ($4 million AAV) with the Stars on Sept. 1.
NHL.com independent correspondent Taylor Baird contributed to this report
