Angeleri is due to travel to Wearside this weekend to complete the technicalities of a £1.5m move from Estudiantes.
Black Cats officials have already agreed the terms of the deal with the Argentinian side, but the transfer has remained on ice while Angeleri has pursued an Italian passport which would remove the need for a work permit.
The 27-year-old right-back first joined Estudiantes in 2002, and while he is looking forward to testing himself in England with a four-year deal at the Stadium of Light in the offing, he admits it will be a wrench to leave his hometown team in Argentina.
I have been longing for a sale to happen because I want to look for new horizons in Europe,
said Angeleri, who won the Argentinian league title in 2006 and the Copa Libertadores in 2009. But I will always have a strong feeling for this club (Estudiantes).
I am cutting my roots and leaving many things here, but one day I will return.
A number of English clubs were linked with Angeleri last summer, but any prospective deal was scuppered when an injury sustained during the latter stages of the Copa Libertadores took longer than expected to heal.
He remained in Argentina, but is poised to become one of two right-backs to join Sunderland, with Egyptian Ahmed al-Muhammadi set to sign a season-long loan.
Steve Bruce is also expected to sign a centre-half this summer, and is understood to be considering a move for Matthew Upson.