The highly-rated 21-year-old, who has represented Argentina at both Under-17 and Under-20 level, will join the Serie A side with the potential for them to make the signing permanent at the end of the season.
Cirigliano, who was born in Buenos Aires, began his career with River Plate and made his senior debut in 2010.
The young midfielder had declared a desire to move to Spain at the end of June, but despite reported interest from a variety of Premier League sides including Manchester City and Arsenal, opted for Verona.
His decision could be down to his wish to play regularly - something that may have been beyond his reach at the Etihad Stadium or Emirates Stadium.
The Argentine will be unveiled by Verona on Thursday.