He said: "This has been a tough decision. I'm sick and tired of giving the government the benefit of the doubt."
Mr Marsden's defection will have no real impact on Labour's overwhelming parliamentary majority - but it comes as an embarrassment to the government, just as its controversial anti-terrorism bill faces opposition from an all-party coalition in the Lords.
The switch follows the earlier defection of members of the breakaway Pro-European Conservatives - including a former Tory MP and MEP - to the Lib Dems.
'Verbal attacks'
Mr Marsden had been due to meet Labour chief whip Hilary Armstrong to discuss allegations he had made against fellow Labour MPs, whom he said attacked him verbally and physically because of his stance on anti-terror legislation.
Mr Marsden, who held his seat with a majority of 3,579 at the last election, said in a statement released by the Lib Dems: "Labour's let people down. But there is an effective alternative.
"Having thought about this over many months, I am convinced that the Liberal Democrats stand for honest and credible policies which can change this country for the better.
"The values which I find most important in politics are tolerance and integrity.
"I have experienced enough Labour intolerance in recent weeks to last a lifetime."
'Team player'
Labour party chairman Charles Clarke said: "Paul Marsden...was not treated any differently to anybody else by the whips.
"The concerns that we have had as a party is that he wasn't prepared to act as a team player.
"That includes the ability to discuss any issues he wants. His allegations are not well-founded."
'Nervous breakdown'
Mr Clarke denied Labour MPs had been briefing against Mr Marsden and sugggesting to journalists that he was on the verge of a nervous breakdown.
"Paul Marsden decided to leave the Labour Party because he didn't agree with the conduct of our war against terrorism and the various aspects of our consequent legislation. I regret that," Mr Clarke said.
"I believe it's his opposition to that war against terrorism which has been the deciding factor in his decision to leave the party," he added.
'Arrogant' Blair
In his defection statement Mr Marsden added: "I want to belong to a party which encourages debate and practises genuine internal democracy.
"His party believes in threats and intimidation to crush internal dissent."
This is the first time since the creation of the Liberal Democrats that a Labour MP has defected to join it.
The last Labour MP to defect to the Liberals - which merged with the Social Democratic Party to form the Liberal Democrats - was Christopher Mayhew, MP for Woolwich East in 1974.
The Lib Dems also unveiled defections on Monday from the Pro-European Conservative Party, led by breakaway Tory MEP John Stephens.
The seven-strong group includes Sir Anthony Meyer, the ex-Tory MP who once stood as a "stalking horse" candidate against Margaret Thatcher for the Tory leadership.
'Anti-war campaigner'
Tory chairman David Davis said the defection proved the Lib Dems were a "left-wing party elected with right-wing votes".
"His is yet one more conflicting opinion in a party full of dissenting voices.
"Liberal Democrats try to be all things to all people. Today's events prove it."
'Betrayal'
Danny Moore, the Labour leader of Shrewsbury and Atcham Borough Council, said he was disappointed at Mr Marsden's decision and called it a "betrayal".
"My feelings at the moment are ones of disappointment and regret that Paul couldn't have had the courtesy to talk this issue through with senior members of the constituency party.
"To reflect Paul's own view, having accused myself and other party members of betrayal, there is no other greater act of betrayal than this."
Mr Moore added: "If Paul Marsden has any degree of credibility left within him, he ought to consider standing down completely, fighting a by-election on a Liberal Democrat ticket and not betray the constituents of Shrewsbury and Atcham who voted for him in June this year."