Villas Boas has signed an two-year contract, Porto said in a statement.
The 32 year-old, a former assistant and scout for Mourinho with Porto, Chelsea and Inter Milan, made his debut as head coach when he took over at Academica Coimbra in October.
He took the side from the relegation zone to an 11th place finish in the Portuguese league.
Porto sacked coach Jesualdo Ferreira last month after the side finished third in the league, behind Benfica and Braga, and missed out on a Champions League spot.
Ferreira had led Porto to three consecutive title wins in the previous seasons.
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