Dickinson, a restricted free agent, had an arbitration hearing scheduled for July 20.
"Jason is a conscientious player who plays a very detailed, 200-foot game," said general manager Jim Nill. "As last season progressed, he began impacting games night in and night out, and he really established himself during the playoffs. We fully expect him to continue to build upon that and be a big part of our team for years to come."
The former 29th overall pick recorded 22 points in 67 games during his first full NHL season in 2018-19. The 24-year-old added five points in 13 playoff games with the Stars.