The 27-year-old has signed a three-year deal with the Wearsiders and joins for an undisclosed fee.
Angeleri has been training with Sunderland for some time, but had been unable to formally sign because his Italian passport, to which he is entitled through his father, had not been issued.
But with the paperwork now completed, Angeleri has become Steve Bruce's fifth summer capture following the acquisitions of Titus Bramble, Simon Mignolet, Cristian Riveros and Ahmed Al-Muhammadi.
Bruce said: "Marcos is a strong, powerful defender and will add depth to the squad.
"He is also very keen to get forward from that position so that adds an extra dimension to the side.
"He has been one of the best right full-backs in South America in recent years and has really impressed us when we've watched
Angeleri began his career at Primera Division side Estudiantes in 2002 and has amassed 175 appearances for the 2009 Copa Libertadores champions.
The defender, who has won three international caps, missed out on Diego Maradona's squad for the World Cup after injury ruled him out of key qualifiers against Colombia and Ecuador in the run-up to the tournament.