Diaz hit .313 with 13 homers and 58 RBIs last season, when he made $1,237,500.
Johnson batted .224 eight homers and 29 RBIs, losing his starting job to Martin Prado. He can sign with any team starting Sunday.
Atlanta also failed to offer a contract to outfielder Ryan Church, who was designated for assignment earlier in the week. Acquired from the New York Mets on July 10 for Jeff Francoeur, Church hit .260 with two homers and 18 RBIs in 44 games with the Braves.