The Athletics claimed Alexander off waivers Wednesday and assigned him to Triple-A Las Vegas.
The Royals released Alexander on Tuesday.
Alexander was designated for assignment by the Royals on Saturday, Jaylon T. Thompson of The Kansas City Star reports.
The Royals optioned Alexander to Triple-A Omaha on Friday.
Alexander is not in the lineup for Friday's contest against the Guardians.
Alexander is out of the lineup for Wednesday's game against the Marlins.
The Royals selected Alexander's contract from Triple-A Omaha on Monday.
Alexander was traded to the Royals on Monday, Jeff Passan of ESPN.com reports.