In a tweet, Peru's current President Francisco Sagasti said he welcomed the announcement.
Mr Castillo rose into the national scene four years ago when he had led thousands of teachers on successful strike over pay.
During his presidential campaign, Mr Castillo pledged to nationalise Peru's lucrative mining and hydrocarbon sectors, and said he would aim to create a million new jobs in a year.
He also proposed to re-introduce the death penalty to help tackle crime.
Mr Castillo won last month's election by a margin of only 44,000 votes - beating Ms Fujimori in her third bid for the presidency.
He claimed victory earlier, but a series of legal challenges by Ms Fujimori delayed an official verdict from election officials.
Ms Fujimori had provided little evidence of her claims of election fraud, and Castillo's Free Peru party has rejected the accusations. Electoral observers, including the Organisation of American States, have also said they have found no irregularities.
Ms Fujimori is the daughter of former President Alberto Fujimori, who is in jail serving a 25-year sentence for crimes including corruption and human rights abuses.
Ms Fujimori herself is being investigated for alleged corruption and money laundering, which she says are politically motivated. Her failure to become president means prosecutors can now proceed with the charges against her.