The former Bolton full-back has completed a medical on Wearside and will officially join the Black Cats' squad when the winter transfer window opens.
Manager Gus Poyet said: "I can confirm Marcos is going to be with us for the rest of the season on loan from Fiorentina, which is something very important.
"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."
Alonso will become Poyet's first signing since he replaced Paolo Di Canio at the helm in October.