The deal is worth $1.25 million, a source told ESPN.com's Pierre LeBrun.
Dillon, 23, had career highs in most categories, including 17 points on six goals and 11 assists last season. He played in 80 regular-season games before the Stars lost to Anaheim in their first playoff series since 2008.
Dillon has 25 points in 129 career games over three seasons. He was fourth among NHL defensemen with a plus-20 rating at home last season.
The Associated Press contributed to this report.