Kostka inked a deal with Skelleftea AIK of the Swedish Hockey League on Sept. 1, TSN reports.
The Senators have traded Kostka along with forward Curtis Lazar to the Flames for blueliner Jyrki Jokipakka and a second-round draft pick, TSN.ca reports.
Kostka was assigned to AHL Binghamton on Wednesday and will have to clear waivers Thursday to make it official, Bruce Garrioch of the Ottawa Sun reports.
Kostka signed a one-year, two-way contract with the Senators on Friday. The contract is worth $800,000 in the NHL and $325,000 in the minors.
Kostka (undisclosed) will return to the lineup Saturday afternoon versus the Flyers, Bruce Garrioch of the Ottawa Sun reports.
Kostka is dealing with an undisclosed injury that will prevent him from suiting up Thursday night against the Wild, Bruce Garrioch of the Ottawa Sun reports.
Kostka impacted the scoresheet for the first time this season, registering an assist in Tuesday's 4-2 loss to the Capitals.
Kostka was called up from AHL Binghamton early Saturday morning.
Kostka is returning to the AHL following a brief stint with Ottawa.
Kostka was recalled by the Senators on Wednesday, Bruce Garrioch of the Ottowa Sun reports.