The Diamondbacks got Johnson in a trade with Houston on Sunday.
The 35-year-old Overbay batted .292 in 45 games with two homers and 11 RBIs. He started 21 games and was used mostly as a pinch-hitter.
Overbay began his big league career in 2001 with Arizona, then had stints with Milwaukee, Toronto and Pittsburgh before returning to the Diamondbacks last August as a free agent.
Johnson batted .279 with eight homers and 42 RBIs this season for the Astros. He made his Diamondbacks debut in the opener of a three-game series at Dodger Stadium.