The 25-year-old centre was previously acquired by Seattle on June 21 from the Chicago Blackhawks in exchange for forward Andre Burakovsky. Veleno finished the season in Chicago after a deadline deal sent him to the Blackhawks from the Detroit Red Wings.
Across 71 games between Detroit and Chicago, Veleno scored eight goals and 17 points.
This coming season was expected to be the final year of a two-year, $4.55-million deal he inked while with Detroit before he was bought out.
Veleno spent the first four-and-a-half seasons of his career with the Red Wings, peaking with a 12-goal, 28-point campaign in 2023-24.