"Football has lost a legend. But Eusebio's place among the greats will never be taken away," said Blatter.
The Portuguese government announced a three-day national mourning for Eusebio's death, with flags in Lisbon to fly at half mast.
Born in Maputo's suburb of Mafalala on Jan 25, 1942, when Mozambique was still under the Portuguese rule, Eusebio rose to prominence as a teenager through his performances for Sporting Lourenco Marques, a team with links to Sporting Lisbon.
European football body UEFA president Michel Platini said: "Football has lost one of the greatest players ever. On the field, Eusebio was a true legend. But also off it, he was a true ambassador for Portuguese football on the international stage. He was more than a footballer."
Football has lost a legend: FIFA president Sepp Blatter
Mozambique President Armando Gebuza said: "He's a figure who has contributed to the deep and rich history of Mozambique. Eusebio came here from time to time. He always maintained a link with Mozambique. He's a very well known and respected figure in our country."
After Mozambique's independence in 1975, Eusebio opted to stay in Portugal, as a Portuguese citizen.The Mozambican legislation did not allow dual nationality at that time, so Eusebio automatically lost his Mozambican citizenship.
But when he visited Mozambique in 1985, the then President Samora Machel offered him a Mozambican diplomatic passport.
Eusebio had said that when he died, his coffin should be covered with the flags of Benfica, Mozambique and Portugal.