O'Neill, whose permanent return was confirmed on 11 June, signed a one-year contract with the option of an additional year.
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Maloney and McManus were promoted from within the club to support O'Neill during his interim spells last season, while former Huddersfield Town. boss Fotheringham later joined the coaching team.
Meanwhile, coach Gavin Strachan has left to join West Bromwich Albion. O'Neill replaced Brendan Rodgers and Wilfried Nancy before guiding Celtic to a Scottish Premiership and Scottish Cup double.
