Moylan, 37, pitched 10 1/3 innings for the Braves last season after recovering from his second Tommy John surgery. He yielded four earned runs on 12 hits and no walks while striking out eight. The right-hander also spent some time with Triple-A Gwinnett.
Moylan will have to prove his durability and skill during spring training with the Royals. If he is able to pass muster, the veteran could serve as bullpen depth during the season.
Bowden notes that the Marlins signed lefty pitcher Jo-Jo Reyes to a minor league deal as well.