The 35-year-old was released by West Brom in March for gross misconduct following the controversy surrounding his "quenelle" celebration after he scored against West Ham in December.
The former France international has since been on the lookout for a new club and seemed set to move to Brazil following talks between the club and his agent. However, despite his representatives signing a pre-contract with Mineiro on April 4, Anelka delayed meeting the Belo Horizonte side for further talks.
Galo director of football Eduardo Maluf explained: "They told us he was to come the following week and stay in Belo Horizonte, visiting our training grounds and looking for houses.
"We said that yesterday was the deadline for an agreement or explanation, as we would like to have him onboard for our Libertadores bid. Today, however, we received an email from Mr. Casini, saying that Anelka, a muslim, was in Kuwait for an event and would only come on the 19th.
"He had the obligation of informing us about this, but we only heard about it now. I talked to our president [Alexandre Kalil, who announced the deal on Twitter], and we agreed that Atletico's greatness is much bigger than a single player and, therefore, we are canceling our commitment."