The move brings to an end the longest current Football League managerial term.
Still guided the Daggers into the ’92 club’ and the Essex side even enjoyed a season in League One in 2010-11, but were unable to avoid relegation back to League Two.
The 62-year-old also helped Maidstone United earn league status back in 1989, and was in his second spell as Dagenham boss after returning to Victoria Road in 2004.
Paul Buckle left Kenilworth Road last week despite an impressive FA Cup run which took in upsets of Wolves and Premier League side Norwich City.
Still will now attempt to succeed where Mick Harford, Richard Money, Gary Brabin and Buckle failed over the last four years and restore the Hatters’ league status.
Dagenham are currently 16th in League Two, eight points clear of the drop zone into the Conference where Luton currently reside in eighth, 11 points off the play-offs but with three games in hand on some of the sides above them.