The right-back, who is currently on the books of Estudiantes, is ready to finish the formalities of his switch to the Stadium of Light in the next 48 hours as Steve Bruce continues to build a squad that he hopes will be capable of pushing towards Europe.
Egypt international Ahmed Al-Muhammadi has agreed a season-long loan at Sunderland, while Cristian Riveros and Simon Mignolet have also signed deals in the North East.
West Ham's Matthew Upson is understood to be a target of Bruce, but Angeleri is on the verge of becoming the next arrival and the 27-year-old is looking forward to the challenge of English football.
A three-year deal is reported to have been agreed and Angeleri said at a press conference in South America: "I am leaving to search for new horizons and progress in England.
"It was Sunderland's proposal that convinced me most. The club interested me, along with the chance to play in the Premier League - and Estudiantes didn't have objections to me being transferred.
"In England they have many cups and tournaments which means many matches and there will surely be the opportunity to play.
"I believe it is a league similar to the style of play that I have at the moment and because of that I don't think it will be hard for me to adapt."
However, Angeleri, who was expected to be named in his country's World Cup squad before being overlooked by Diego Maradona, does expect to go back to Argentina later in his career.
He added: "I am leaving here with many things, but one day I am going to return because Estudiantes is my second home.
"Perhaps I will return to Estudiantes as a player, as a worker for the club, or as a visitor, but I am always going to return."