Both players will now become unrestricted free agents.
Strome, 25, had a slow start to last season but finished the year with 48 points and a career-high 22 goals after being promoted to the top line between Patrick Kane and the since-traded Alex DeBrincat. His qualifying offer would have been worth $3.6 million.
Kubalik, 26, had 15 goals and 32 points last season and has seen his scoring totals decline since he scored 31 goals and was a Calder Trophy finalist three seasons ago. His qualifying offer was worth $4 million.
Earlier in the day, the Blackhawks placed forwards Brett Connolly and Henrik Borgstrom on waivers for the purposes of a buyout.
Last week at the draft, the Blackhawks traded star scorer DeBrincat to the Senators for draft picks — including the seventh overall selection which they used on defenceman Kevin Korchinski — and young centre Kirby Dach to the Canadiens for draft picks — including the 13th overall pick, which became forward Frank Nazar.