The left-back, who plays for Italian club Fiorentina, has passed a medical and agreed a deal until the end of the season.
Alonso is Gus Poyet's first signing as Sunderland manager and returns to England six months after leaving Bolton for Serie A.
"I can confirm Marcos is going to be with us for the rest of the season," said Poyet.
"I was looking for a player in that position on the left side and I hope he will help us and everybody will like him.
"I am delighted that everything is agreed."
Poyet and predecessor Paolo Di Canio have used a number of different players at left-back this season.
The only specialist in that position, Italian Andrea Dossena, has started just five league games since arriving in the summer.