The 66-year-old from Northern Ireland will replace Spanish coach Aitor Karanka, who parted company with Forest after 12 months in charge at the City Ground.
O'Neill takes charge of Forest with the club sitting ninth in the second division, four points outside the playoff places.
"With his commitment to the club, knowledge of the game and passion to succeed, O'Neill will be aiming to take the club back into the top flight of English football," the club said in a statement.
O'Neill will be returning to club management for the first time since a mixed spell at Sunderland, which he helped steer away from the relegation zone in his first season before it struggled again prior to his sacking in March 2013.
In a managerial career stretching over three decades, O'Neill has twice won the League Cup with Leicester City and led Celtic to three Scottish Premiership titles, three Scottish Cups and a League Cup.
According to British media reports, O'Neill could be joined by his former Ireland assistant Roy Keane, who made his breakthrough as a midfielder at Forest between 1990 and 1993 before moving to Manchester United.
(Reporting by Hardik Vyas in Bengaluru; Editing by Christian Radnedge and Hugh Lawson)
