The 25-year old, who is joint top scorer in the African zone World Cup qualifiers with five goals, has signed a contract that includes a US$40m buy-out clause.
He told the club's website: "Sporting has one of the best schools in the world, where players like Cristiano Ronaldo, Nani and Luis Figo come from.
"It is an honour to use this shirt and to be part of this family."
Slimani spent four seasons with CR Belouizdad, scoring 32 goals in 96 appearances for the Algiers-based club. He previously played for JSM Cheraga.