Boxberger, who had joined the Royals on a one-year, $2.2 million contract after earning 32 saves as the Arizona Diamondbacks' closer in 2018, had a 5.40 ERA with one save and three blown saves in 29 games this season.
In January, Skoglund was suspended for the first 80 games of 2019 after testing positive for two performance-enhancing substances.
Skoglund, 27, who was 1-6 with a 5.14 ERA last season, was optioned to Triple-A Omaha.
Left-hander Tim Hill was recalled from Omaha in a corresponding move. He has a 6.75 ERA in four innings (six games) for Kansas City this season.