According to reports in the Peruvian media, former Chile and Athletic Bilbao head coach Marcelo Bielsa had been the FPF's preferred option but once the 58-year-old Argentine rejected Peru, Bengoechea was announced.
The 49-year-old replaced compatriot Sergio Markarian, who resigned in October after failing to take Peru to the 2014 World Cup.
Bengoechea was Markarian's assistant coach in the Peruvian national setup since 2010, while he had also spent time working under the 69-year-old at Universidad de Chile.
The FPF confirmed the appointment in a statement, revealing Bengoechea could have his contract extended to include the 2015 Copa America, which will be held in Chile.
Bengoechea represented Uruguay 43 times between 1986 and 1997, while his club career included significant stints at Sevilla and Penarol, where he was known as 'the Professor'.
"The FPF is grateful to Professor Bengoechea for accepting this position," FPF president Manuel Burga said in a statement.
"And we are confident that with the cooperation of all, we will achieve our cherished desires."
