Announcing a new date, Mrs May said the EU had made it clear the Irish backstop was "not a plot to trap the UK" and urged MPs to see Brexit through.
Labour had threatened to force a confidence vote in the PM if she did not set a date for the vote.
Labour leader Jeremy Corbyn said Mrs May had "led the country into a national crisis" and she no longer had cabinet backing.
He said a month would have been wasted since the original 11 December vote was postponed, with "not a single word renegotiated and not a single reassurance given".
"The deal is unchanged and is not going to change," he said. "The House must get on with the vote and move to consider the realistic alternatives."
In a Commons statement, Mrs May said MPs would resume the debate on her Brexit deal - which was halted last week - in the week of 7 January with "meaningful" vote taking place in the following week.
She said she had won fresh guarantees at last week's EU summit over measures to avoid a hard border on the island of Ireland and hoped to secure additional "political and legal assurance" in the coming weeks.
She ruled out the case for another referendum, saying a fresh vote would do "irreparable damage to the integrity of our politics" and not settle the issue. [...]
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