Buckle, who led Torquay United to the Football League and was last in England with Luton Town, fills the void left by the sacking of Yates on Tuesday after five years in charge.
A run of just two wins from 12 League Two fixtures saw Yates' tenure come to an end, with Buckle agreeing a 12-month rolling contract.
A statement read: "Cheltenham Town have appointed former Torquay United, Bristol Rovers and Luton Town manager Paul Buckle as their new manager.
"Paul, 43, has agreed a 12-month rolling contract at Whaddon Road and will take charge of his first match against Oxford United at home on Saturday (3pm)."
Cheltenham sit 18th in the fourth tier following a four-game losing streak.