Howard signed with the Tohoku Rakuten Golden Eagles of the Nippon Professional League in Japan on Sunday.
The Giants signed Howard to a minor-league contract Thursday.
Howard elected free agency Monday after he was outrighted off the Guardians' 40-man roster.
The Guardians designated Howard for assignment Sunday.
Howard is listed as the Guardians' scheduled starter for Thursday's game against the Tigers in Detroit.
The Guardians acquired Howard from the Giants in exchange for cash considerations.
Howard was designated for assignment Sunday by the Giants, Shayna Rubin of the San Francisco Chronicle reports.
Howard allowed six runs on six hits and two walks while failing to record a strikeout over 2.2 innings in a no-decision versus the Dodgers on Saturday.
Howard is slated to be the Giants' primary pitcher in Monday's game against the Cubs, Alex Pavlovic of NBC Sports Bay Area reports.
Howard is expected to serve as the Giants' bulk reliever Wednesday against the Cubs behind opening pitcher Erik Miller.