The former Brazil and AS Roma midfielder, who won the Brazilian championship three times as a player with Internacional, is charged with retaining the Libertadores Cup the club won for the second time last year.
The 57-year-old Falcao, who has not worked as a coach since the first half of the 1990s when he had spells in charge of Brazil, Internacional and Japan, replaces Celso Roth who was sacked on Friday.
"Reds fans are called on to come to the Beira-Rio stadium on Monday to greet their eternal idol and now coach of Internacional, Paulo Roberto Falcao," the club from the southern Brazilian city of Porto Alegre said on their website.
Falcao played for a brilliant Brazil side at the 1982 World Cup in Spain and was also in the team four years later in Mexico. He helped Roma win the Serie A title in 1983.
Internacional face Emelec of Ecuador at home on April 19 in their final Libertadores Cup Group Six match after losing away to Chiapas of Mexico last Wednesday when a draw would have secured their placed in the last 16.
Inter lead the group with 10 points, one more than Chiapas and two ahead of Emelec.
Playing under caretaker coach Andre Doring on Sunday, Inter crushed Canoas 6-2 in the Gaucho (Rio Grande do Sul) state championship.
