In 1992, he earned a Master's in Public Administration from the John F. Kennedy School of Government at Harvard University.

He ran unsuccessfully for mayor of Lima in 1983, losing to the left-wing candidate Alfonso Barrantes Lingán.

Barnechea was elected to Peru's lower house of the Congress in 1985 and took office on 26 July 1985 during the government of President Alan García.

However, on November 23, 2020, six days before the internal electoral process of Popular Action, Barnechea announced that he was resigning from the candidacy for the Presidency of the Republic, for disagreeing with the decisions made by the Popular Action group and that led to the presidency of the Republic to Manuel Merino, as well as the divisions within the party.

Barnechea is married, since 1983, to Claudia Ganoza Temple, a former step-daughter to United Nations Secretary General Javier Pérez de Cuéllar (1920-2020).