The Yankees made the moves before Thursday's game against Houston.
Wheeler homered in his major league debut on July 3. He hit .267 with two homers in 16 games for the Yankees.
Yankees manager Joe Girardi said he wanted an extra right-handed bat with New York set to face three lefty starters in four days.
Whitley was 4-3 with a 5.43 ERA in 19 games, including 12 starts. He had been almost exclusively a reliever in his pro career until this season, when he reached the majors for the first time.