Chatham agreed to a minor-league contract with the Diamondbacks earlier this month, Chris Cotillo of The Springfield Republican reports.
Chatham was released by the Phillies on Sunday, Matt Gelb of The Athletic reports.
Chatham was optioned off the Phillies' active roster Tuesday and sent to minor-league camp, Scott Lauber of The Philadelphia Inquirer reports.
Chatham was traded from Boston to Philadelphia in exchange for a player to be named later or cash considerations Monday, Todd Zolecki of MLB.com reports.
Chatham was added to the Red Sox's 60-man player pool.
Chatham is one of a few prospects that could land a spot on Boston's expanded roster, Christopher Smith of MassLive.com reports.
Chatham made 12 starts at second base in the minors last season, then made another 10 starts in the Arizona Fall League, Christopher Smith of MassLive.com reports.
Chatham (shoulder) will start at shortstop in Saturday's spring game against the Yankees, Jen McCaffrey of The Athletic reports.
Chatham (shoulder) will serve as the Red Sox's designated hitter and will bat sixth in Wednesday's Grapefruit League game against the Pirates, Pete Abraham of The Boston Globe reports.
Chatham was scratched from the lineup for Friday's exhibition game against Northeastern University due to a sore right shoulder, Julian McWilliams of The Boston Globe reports.