The government hopes the move will encourage tourism and help revive Brazil's sluggish economy, which is expected to stay in recession for a second year in 2016.
Foreigners who arrive between June and Sept. 18 will be able to stay for up to 90 days without a visa, according to a law already passed by Congress that was signed by Rousseff and published in the gazette.
Diplomats in Brasilia say Western governments are worried about the safety of their athletes and tourists at the games because they believe many Brazilian authorities are complacent, taking too much comfort in Brazil's historical status as an enemy-free nation.
Islamic State militants have stepped up international attacks in recent months. The group claimed a coordinated assault in Paris on Nov. 13 in which 130 people were killed.
Cabinet Minister Ricardo Berzoini said on Monday that Brazil was seeking help from countries with a history of combating terrorism and the director of Brazil's intelligence agency Abin said there is no sign of Islamic State or any other jihadist group in Brazil, the largest country in South America.
Visas will not be required regardless of whether travellers have tickets to Olympic events.
The Olympics will be held between Aug. 5 and 21 and the Paralympic Games follow from Sept. 7-18. Brazil was praised for pulling off a mostly incident-free World Cup in 2014, when only visitors with tickets to games were not required to have visas.
(Reporting by Caroline Stauffer; Editing by Raissa Kasolowsky)
