Babs, who had been suffering from Alzheimer's disease, died at her nursing home early on Tuesday afternoon, her lawyer Thomas Bodström told the Expressen newspaper.
"She died in peace with her family close by," he said.
Babs' daughter Titti was among those on hand at the time of death.
"We are truly glad for these past few months that we shared with our dear mother. She was comfortable and in peace where she was living," she told the paper.
Babs, who hailed from Kalmar in southern Sweden, had a storied career that spanned the music genres, but she found her forte in jazz, where she shared the international stage with greats including Duke Ellington, with whom she had a longstanding artistic collaboration (see video below).
In 1958, Babs became the first Swede to ever represent Sweden at the Eurovision song contest (see video below), where she finished fourth overall singing Lilla stjärna ("Little Star").
In 1972, Alice Babs was awarded the honorary title of Court Singer by King Gustaf VI Adolf. Among other honours, her face now graces the arrivals hall at Arlanda airport.
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She had a slew of Swedish films to her name, including the 1940 hit Swing it, magistern.