The committee, comprising 11 main members and seven substitutes, initially has 180 days to investigate claims that the NSA monitored emails between Rousseff and several of her top aides, and tapped her phone.
The investigative period can be extended by another 180 days if the commission needs more time.
The report was based on documents leaked by Snowden
The members discussed the possibility of the state providing federal protection for Rio de Janeiro-based journalist Glenn Greenwald and his partner David Miranda, considering them to be key witnesses in the investigation. Greenwald was the first to break the story of Washington's global spying programme, based on documents leaked by former NSA contractor Edward Snowden.
Snowden, wanted by the US on espionage charges for revealing the surveillance scheme, has been given temporary asylum in Russia.
Miranda was recently interrogated for nine hours at London's Heathrow airport as he travelled from Germany to Brazil, and had his belongings confiscated.
British officials said they were operating under an anti-terror law, but Greenwald said he believed it was an attempt to intimidate.
The senate's decision to open an investigation follows the broadcast of a Brazilian TV news programme that said the NSA spied on the highest levels of Brazil's government, even the president.
That report was also based on documents leaked by Snowden and made public by Greenwald.
News of the NSA spying on Brazil first broke in July, when Brazil's O Globo daily published articles alleging the US agency had monitored digital communications and phone calls.
Washington has said the spy programme is designed to thwart terrorism, but Brazil said it suspects industrial espionage and has demanded an written official response from the US government.