Infielder Corban Joseph was also outrighted to Triple-A Scranton/Wilkes-Barre, leaving the Yankees' roster standing at 39 players.
Anna, 26, spent the 2013 season with Triple-A Tucson, where he batted .331 (165-for-498) with nine home runs and 73 RBIs in 132 games.
A left-handed batter who saw time at second base, shortstop, third base and left field, Anna was originally selected by the Padres in the 26th round of the 2008 First-Year Player Draft.
The Yankees made the roster moves in advance of Wednesday's deadline to protect eligible players from the Rule 5 Draft, slated to take place on Dec. 12.
Sanchez, Heathcott, Campos and Mitchell are currently listed among the Yankees' top prospects, according to MLB.com.
Sanchez turns 21 next month and is ranked as the team's No. 1 prospect. He combined to bat .253 (115-for-454) with 15 homers and 71 RBIs in 117 games with Advanced Class A Tampa and Double-A Trenton in 2013.
Heathcott, 23, batted .261 (104-for-399) with eight homers and 49 RBIs in 103 games with Trenton in 2013. He is listed as the Yankees' No. 7 prospect.
The 21-year-old Campos is ranked as the Yankees' No. 14 prospect. He went 4-2 with two saves and a 3.41 ERA in 26 games (19 starts) with Class A Charleston in 2013 and was acquired by the Yankees in a January 2012 trade with the Mariners that also netted right-hander Michael Pineda.
Mitchell, 22, combined to go 4-11 with a 4.71 ERA in 27 games (26 starts) with Tampa and Trenton in 2013 and has been tabbed as the Yankees' No. 18 prospect. Greene, 25, combined to go 12-10 with a 3.38 ERA in 27 games (26 starts) with Tampa and Trenton in 2013.
The Padres received the 24-year-old Paullus, who was 6-3 with a 3.01 ERA in 38 relief appearances for Class A Charleston and Tampa in 2013. A 19th-round Draft selection of the Yankees in 2011, Paullus made 32 of those appearances for Charleston.
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.