Ross, 39, has agreed a deal that runs initially until the summer of 2016.
The former St Mirren defender has coaching experience from stints at Dumbarton and Hearts, where he departed in October.
Ross will be in the dugout for Saturday's home match against the Buddies.
Alloa are bottom of the Championship, three points adrift of Livingston, who they beat 1-0 on Saturday.
Scottish Championship strugglers Alloa Athletic have appointed Jack Ross as their new manager following the resignation of Danny Lennon.