The corporation has come to the conclusion after protests from the Conservatives that Sugar's new position as the government's enterprise tsar and his Labour peerage breaks BBC impartiality rules.
The Conservatives have called for Sugar to give up the show, which this year brought the BBC bumper audiences of around the 7m-10m mark from April to June.
Next year's series could clash with a general election, which must be called before June 2010.
However the BBC says that because Sugar is an adviser rather than a member of the government it does not constitute a breach of the rules.
Tory shadow culture secretary Jeremy Hunt said he was not satisfied by the BBC's argument, describing it as "riddled with inconsistencies".
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