Yvette Cooper branded the policy, which was introduced two and a half years ago and sought to send UK asylum seekers to Rwanda for processing, "the biggest waste of taxpayer money I have ever seen".
She told the Commons that over the course of six years the Conservatives had intended to spend £10bn on the policy, but never divulged this figure to parliament.
The home secretary said she had formally notified the Rwandan government that the partnership was over and thanked them for working with the UK "in good faith".
"The failure of this policy lies with the previous UK government, it has been a costly con and the taxpayer has had to pay the price," she said.
Under the Conservatives, the Home Office refused to set out the full cost of the scheme, though an official letter last year stated it had reached £290m. In a report last spring the National Audit Office estimated that the cost of the policy had surpassed £500m.
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