Goeddel was released by the Nationals on Saturday, James Fegan of The Athletic reports.
Goeddel agreed to a minor-league contract with the Nationals, Matt Eddy of Baseball America reports.
Goeddel cleared waivers and was outrighted to Triple-A Louisville on Friday.
Goeddel was claimed off waivers by the Reds on Wednesday, Meghan Montemurro of The News Journal reports.
Goeddel was designated for assignment by the Phillies on Thursday, Matt Gelb of The Philadelphia Inquirer reports.
Goeddel will begin the season at Double-A Reading, Matt Breen of The Philadelphia Inquirer reports.
Goeddel is expected to open the season at Triple-A Lehigh Valley, Ryan Lawrence of the Philly Voice reports.
Manager Pete Mackanin said he was unsure if Goeddel (concussion) will be able to play again this season, Matt Breen of the Philadelphia Inquirer reports.
Goeddel was diagnosed with a concussion Thursday, Jack McCaffery of the Delaware County Daily Times reports.
Goeddel left Wednesday's game after being hit on the side of the helmet by a pitch, Todd Zolecki of MLB.com reports.