Ms Topolansky took over after the resignation of Jose Sendic amid corruption allegations.
A former left-wing guerrilla like her husband, she escaped prison, spent 13 years in jail, and survived torture.
Uruguay has been led by the left-wing Frente Amplio party, which has promoted generous social welfare policies, since 2005.
Under the constitution, Mr Sendic, the former vice-president, should have been replaced by the senator with the most votes in the last elections.
That should have been Jose Mujica, the former president, who became popular across the world for giving away most of his salary and was dubbed "the world's poorest president".
However Mr Mujica is ineligible due to a prohibition on presidential re-election, so the senator next in line was his wife.
Ms Topolansky will also head the Senate and the Uruguayan congress's general assembly.
Mr Mujica and Ms Topolansky were involved in Uruguay's armed insurgency, known as the Tupamaro movement, in the 1960s and 1970s.
Ms Topolansky left her upper class family to join the insurgency, and was nicknamed "La Tronca" ("The Tree Trunk") for her reputation for toughness, after spending time in prison.
She was one of 38 political prisoners involved in a high-profile prison escape from the Carcel Cabildo, a women's prison, in 1971.
The women crawled through excrement and fumes in the sewage pipes for 45 minutes until they reached another tunnel to a safe house dug by comrades on the outside.
However, she was recaptured a few months later, and spent years in solitary confinement.
Ms Topolansky does not talk much about her militant past, but has revealed she took part in armed robberies and for years rumours have circulated she was one of the rebel group's top shooters.
However, her supporters now describe her as a kindly and active member of the Uruguayan upper house.