Tomko had been designated for assignment on June 12, meaning the Royals had 10 days to trade, release, or waive Tomko if he didn't accept a minor league assignment.
The 35-year-old was 2-7 with a 6.97 earned run average in 16 games, including 10 starts. Opponents hit .314 off him. He signed a $3 million, one-year deal in January.
Tomko has also pitched in the majors with the San Diego Padres, Los Angeles Dodgers, San Francisco Giants, St. Louis Cardinals, Seattle Mariners and Cincinnati Reds. He has a 95-99 record in 362 games in the majors.