Cook was released by the Marlins on Monday.
Cook is part of the Marlins' 60-man player pool, Craig Mish of SportsGrid.com reports.
Cook has yet to pitch in a Grapefruit League game due to a toe injury, Joe Frisaro of MLB.com reports.
Cook signed a minor-league contract with the Marlins on Tuesday, Bob Nightengale of USA Today reports.
Cook agreed to a one-year, $1.3 million contract with the Yomiuri Giants, the Japan Times reports.
Cook was outrighted to Triple-A Tacoma on Wednesday, Ryan Divish of The Seattle Times reports.
Cook was recalled from Triple-A Tacoma on Saturday, Ryan Divish of The Seattle Times reports.
Cook was optioned to Triple-A Tacoma on Friday.
Cook (1-0) fired a scoreless eighth inning in a win over the Red Sox on Friday, allowing a hit and two walks while recording a strikeout.
Cook slipped on the dugout steps at Minute Maid park prior to Tuesday's game and initially appeared to be in pain, Ryan Divish of The Seattle Times reports.