The team, however, did announce it will exercise its 2011 club option on pitcher Andrew Brackman.
The Yankees picked up the 34-year-old Berkman at the 2010 trade deadline from the Houston Astros, where he had played for 12 seasons. He had a $15 million team option in his contract that also included a $2 million buyout clause for next season.
Berkman batted .255 with one home run and nine runs batted in in 37 games with New York.
Wood, 33, was also obtained at the trade deadline from Cleveland. He sported a 2-0 record with a 0.69 earned run average in 24 games and was set to make to make $11 million in 2011.
Johnson, meanwhile, missed most of the season with a sore right wrist after being put on the disabled list in May. He hit .167 with two homers and eight RBI in only 72 at-bats over 24 games.
Brackman, the Yanks' first-round 2007 draft pick, put in 27 appearances -- including 26 starts -- with Class A Tampa and Class AA Trenton in 2010 last season.