The 22-year-old Eakin tied for fourth on the team with 16 goals and 35 points in 81 games to help Dallas end a five-year playoff drought. The Stars lost to Anaheim in the first round.
Eakin led the Stars in faceoff wins and total faceoffs taken. He was acquired in the trade that sent Mike Ribeiro to Washington two years ago.
He has 67 career points (27 goals, 40 assists) in 159 games with the Stars and Capitals.
The contract was announced on Monday.