Still, 62, was the fourth longest serving manager in England behind only Sir Alex Ferguson, Arsene Wenger and David Moyes.
But his nine-year spell - a Football League best - in what was his second stint at Victoria Road has come to an end on Tuesday with two-and-a-half-years remaining on his contract.
Still has been lured to Blue Square Bet Premier promotion chasers Luton, with unconfirmed reports suggesting he was offered a bumper £200,000 per year deal to replace Paul Buckle, who left Kenilworth Road last week by mutual consent for unspecified personal reasons.
Still will be unveiled at the new Hatters boss at a 1pm press conference on Tuesday afternoon and Dagenham have confirmed that his assistant Wayne Burnett will serve as their interim manager for the remainder of the season.
"John had two offers on the table for his services and was given permission by the board of directors to talk to Luton Town at the weekend," read a statement on the club's official website, www.daggers.co.uk.
"He has thought over the proposal from the Blue Square Premier side and has decided to take up the new challenge.
"Under the terms of his contract, Dagenham & Redbridge FC were entitled to a large compensation fee from the Hatters but that would have stopped John from being able to make the move.
"In light of the fantastic job he has done for the Daggers, Luton will instead pay a nominal amount up front with further nominal payments depending on their success with John at the helm. The club will also be sending a side to play a pre season friendly at Kenilworth Road."
The statement added: "For continuity, and in recognition of tremendous work he has already shown, the club have today appointed assistant manager Wayne Burnett as the interim manager until the end of the season
"Wayne has impressed the board when deputising for John in the past and has managed at local sides Fisher Athletic and Grays Athletic in the past.
"Wayne's first game will be on Wednesday for the trip to Capital (One) Cup finalists Bradford City."
Still has a wealth of lower league experience and led Dagenham from the Conference to the Football League for the first time in their history in 2007 before then guiding them to League One three years later, although they were quickly relegated back to League Two where they currently remain in 16th place.
It is that success which Luton, currently eighth in the Blue Square Bet Premier, hope to replicate as they bid to return to the Football League following three successive failed play-off attempts.