Toon owner Mike Ashley had been reluctant due to his policy of not spending money on players over 27 years of age.
Lemina turns 28 next month, but the Daily Mail says club staff have been able to persuade Ashley that it is a deal worth completing given the current state of the transfer market.
Gabon international Lemina impressed last season on loan at Fulham.
Nice have also tried to sign the holding midfielder, causing Newcastle to hasten their plans.
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