The Reds outrighted Buchanan to Triple-A Louisville on Tuesday.
The Reds designated Buchanan for assignment Sunday.
The Reds selected Buchanan's contract from Triple-A Louisville on Saturday.
The Phillies traded Buchanan to Cincinnati on Tuesday for cash considerations, Matt Gelb of The Athletic reports.
Buchanan signed a minor-league contract with the Phillies on Tuesday that includes an invite to major-league spring training.
Buchanan re-signed Dec. 8 with the Korea Baseball Organization's Samsung Lions on a one-year, $1 million contract, Jee-ho Yoo of the Yonhap News Agency reports.
Buchanan signed a one-year, $750,000 contract with the Yakult Swallows of the Nippon Professional Baseball League, Corey Seidman of CSN Philadelphia reports.
Buchanan was released by the Phillies on Wednesday.
Buchanan was designated for assignment by the Phillies on Friday.
Buchanan or Adam Morgan are the likely options to replace Zach Eflin in the Phillies' rotation, Matt Gelb of the Philadelphia Inquirer reports.