The Flames sent a fourth-round pick in Friday's NHL entry draft to the Kraken in exchange.
Seattle selected Pitlick, 29, from the Arizona Coyotes in Wednesday's expansion draft.
The six-foot-two, 200-pound centre had 11 points (six goals, five assists) for the Coyotes last season.
Pitlick was originally selected by the OIiers in the second round of the 2010 entry draft (31st overall) and has split 286 NHL games between Edmonton, Dallas, Philadelphia and Arizona, notching a career 84 points (47 goals, 37 assists).
He's signed through next season at a cap hit of US$1.75 million.
The Flames lost captain Mark Giordano to the Kraken in Wednesday's expansion draft, opting against protecting the 37-year-old who has spent his entire 15-season career in Calgary.