The Portuguese, now with Real Madrid, was given the accolade after leading Inter Milan to a treble of Champions League, Serie A and Italian Cup last season.
He won the poll ahead of two Spaniards, Vicente del Bosque, who led Spain to last year's World Cup, and Barcelona coach Pep Guardiola.
Former Chelsea coach Mourinho, 47, has won the Champions League with two different clubs having previously led Porto to the title.
The new award was organised by FIFA in conjunction with France Football magazine.
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