Forlan's father and grandfather were also South American champions with Uruguay over a period spanning the 95 years of the world's oldest active tournament.
"My generation, my grandfather, my father and I have gone down in football history," Forlan told reporters after Uruguay's victory at River Plate's Monumental packed with 55,000 fans.
"It makes me very proud that my grandfather was a champion, my father too, it doesn't happen every day," he said after contributing two goals to Uruguay's 3-0 win over Paraguay in the final.
Forlan ended a year without scoring for his country and his two goals put him equal as Uruguay's top international marksman with the late Hector Scarone, a World Cup and double Olympic football title winner between 1924 and 1930.
His maternal grandfather Juan Carlos Corazo and 66-year-old father Pablo, a defender at the 1966 and 1974 World Cups, played in Uruguayan sides that won the South American crown.
The 32-year-old Forlan, capped a record 82 times, also followed his grandfather's footsteps at club level by starting his career at Argentina side Independiente in Buenos Aires before embarking on a European career that has taken him via Manchester United and Villarreal to Atletico Madrid.
Uruguay's 15 titles, one more than hosts Argentina whom their upset on penalties in the quarter-finals, include winning in 1987 beating Chile at the Monumental in Buenos Aires and their last at home in 1995 when they beat Brazil at the Centenario in Montevideo.
