It was the first time in 15 years that Labour has won a House of Commons seat from the Tories in a by-election.
Victorious candidate Andy Sawford suggested it had set the party on track for a successful general election in 2015, declaring: "The road to Downing Street runs through Corby."
The by-election in the Northamptonshire seat, which has strong Scottish connections through its steelworks background, was forced by the resignation of Conservative MP Louise Mensch to spend more time with her family in the USA.
Last night she took to Twitter to accept the blame for her party's failure to retain the seat, which was Labour from 1997 until 2010.
But Mr Sawford said the result was "a damning verdict on (David) Cameron's betrayal of the British people".
Mr Sawford won 17,267 votes, against Conservative Christine Emmett's 9,476, on a 12.67% swing from Tories to Labour, overturning a Tory majority of 1,951 in the 2010 general election.
Liberal Democrats were beaten into fourth place by the UK Independence Party, and Nick Clegg's party suffered the indignity of losing its deposit, despite requesting two recounts.
Shadow business secretary Chuka Umunna dismissed Tory claims that the by-election was a verdict on resigned MP Louise Mensch, insisting it was an endorsement of Labour under Ed Miliband.
"The only person that residents and voters in Corby were talking to me about were David Cameron and George Osborne," he said.
"This is a damning indictment of their failed economic plan, which is hitting people really hard, people are losing their jobs, people are paying huge tuition fees - and in addition to that, it's a continuing endorsement of Ed Miliband's leadership.
"Generally, Corby has voted for the winning party and this is Labour winning back support in a key seat with the key demographics that we need to win support from to win a majority in the next general election. It's good progress."
Mr Sawford said the result was a "damning verdict", delivered by middle England, on David Cameron's premiership.
In his victory speech, he said: "This result is a historic gain for today's One Nation Labour Party.
"Today, Middle England has spoken and they have sent a very clear message to David Cameron."
He added: "Make no mistake, since this constituency existed, no party has formed a government without winning. The road to Downing Street runs through Corby."
Mr Sawford said the result showed that Labour, under Mr Miliband, was earning back the trust of the voters it had lost in 2010.
"This result is a damning verdict on Cameron's betrayal of the British people," he added.
Responding to the Corby result, Prime Minister David Cameron said: "It's a classic mid-term result and obviously made difficult by the fact that the Conservative MP left the seat in question.
"Obviously with mid-term results you listen carefully to what people are saying but when I look across the country and see that Labour haven't won in Bristol, can't win in Swindon, can't win in the middle of Wales, I think it is a very mixed picture and shows there is no enthusiasm for the alternative.
"What the Government needs to do is keep going with the very important plans we have to get our economy and country back on track."
Conservative sources suggested Labour had failed the so-called "Crewe Test" in Corby. For Mr Miliband's party to be doing well in mid-term, it needs to be able to match the Tory performance in the 2008 Crewe by-election, when they took the Cheshire seat from Labour on a swing of more than 17.6%, said a party source.
Labour's swing is comparable to the Monmouth by-election of 1991, when the Conservatives went on to regain the seat and hold on to power in the 1992 general election, said the Tory source.
Adam Lotun, who fought on a disability rights ticket with backing from Scottish groups, came second last, taking only 35 votes.
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