He said he was forcing a by-election to protest against the "insidious" erosion of civil liberties in Britain.
In his statement, Mr Davis said that until last night he believed Parliament was engaged in a "noble endeavour".
"I will argue in this by-election against the slow strangulation of fundamental British freedoms by this government," he added.
Mr Davis spearheaded the Conservatives' failed bid to defeat the Government over extending detention without charge, which caused disquiet among some Tory MPs.
As the resignation drama unfolded in Westminster, a Lib Dem spokeswoman confirmed the party would not be fielding a candidate in the resulting Howden and Haltemprice by-election - giving Mr Davis a clear run against a Labour candidate.
Mr Cameron, who promoted the shadow attorney general Dominic Grieve to take over from Mr Davis, described Mr Davis's decision as "courageous" and "wished him well", but insisted he had to have a "permanent" shadow cabinet.
"I wish David Davis well in his by-election campaign. I know the Conservatives - including me - will want to go and support him," Mr Cameron told reporters. "But my responsibility at all times is (to have) that strong permanent team ready for government."
Mr Davis's local party fully backed his decision, its chairman Duncan Gilmour said.
"David discussed early in the week what he would do if the result went against us last night. David is a man of principle and we fully back him," he told the Press Association.
Liberal Democrat leader Nick Clegg said: "David Davis's decision to resign his seat and fight a by-election over the issue of 42 days is a dramatic move. I am grateful to him for having informed me following the vote of his intention to take this step.
"The Liberal Democrats have consistently opposed this unnecessary and illiberal proposal which poses a threat so serious to British liberties that it transcends party politics.
"I have therefore decided, after consultation with the party nationally and locally, that we will not stand a candidate at the forthcoming by-election which will be contested by David Davis solely on this issue.
"The Liberal Democrats will of course fight the Haltemprice and Howden seat as vigorously as ever at the next General Election."
The Lib Dems had targeted the seat in 2005 as part of its ill-fated "decapitation" strategy to unseat key Tory figures but Mr Davis was re-elected with a 5,116 majority.
The former home secretary David Blunkett dismissed the resignation as a "childish and immature" publicity stunt and urged his Labour party not to use public money to field a candidate in the by-election.
"David Davis's behaviour is a pure piece of political theatre, even more bizarre than John Major resigning as leader of the Tory Party in order to stand again against his own colleagues," he said.
"It is my view that neither the Labour Party nor the Liberal Democrats should give him the egotistical satisfaction of a contest in which he costs the public purse, as well as political parties, substantial sums of money to make exactly the same point that he's already been putting very strongly as shadow home secretary."
The communities secretary Hazel Blears said: "The Tories are plainly in disarray and confusion over the serious issue of national security."
Aides to Mr Davis had indicated that last night's vote was "do or die", and he had staked a great deal of his credibility on the outcome.
Privately Mr Davis has accepted that many on the Tory benches were uncomfortable about opposing tough law and order measures.
However, he is seen as one of the Shadow Cabinet's best operators, and has claimed the scalps of a succession of Home Secretaries.
His popularity among the Conservative grass roots was demonstrated when he came runner-up to David Cameron for the party leadership in 2005.
Mr Davis worked very closely with pressure group Liberty in mounting opposition to the proposals.
Liberty director Shami Chakrabarti said: "Last night's debate, and the brave Labour rebels in particular, showed that democrats from across the spectrum care passionately about rights and freedoms.
"MPs of all parties hold courage and conviction about these values and few more so than David Davis."
She said the 42-day policy was a "divisive and counter-productive folly and not the first of its kind".
"Liberty and security can go hand in hand; we don't defeat terrorism by bowing to it."
The Tory MP for Spelthorne, David Wilshire, said: "I am saddened that a good friend feels compelled to take such a drastic step, but I understand how strongly he feels about this abuse of human rights and the rule of law and I respect him for putting his beliefs before his personal interests.
"I sincerely hope we will be able to welcome him back soon."
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