The 34-year-old arrives at the Stadium of Light on the back of a season-long spell at Napoli last term, having also spent 10 years with Lyon, and the Uruguayan is delighted to have found such a player.
"We looked at a few different options, but I think that straightaway, because of his pedigree and the way he plays, Anthony was always our first choice," he told the Sunderland Echo.
"We knew we were already a bit short and as soon as Billy got injured, that was the final confirmation that we needed to look at options to bring in a player.
"After analysing the market with Lee Congerton and company, we decided that Anthony was the best option. We were lucky to convince him to come with us."
The Frenchman, who has 20 caps for Les Bleus in an 11-year international career, could make his debut at home to Arsenal tomorrow.