The announcement was made the day after the actor won the Golden Globe award for Best Actress in a Television Series Musical or Comedy for her role in The Marvelous Mrs Maisel.
Brosnahan stars in the series as Fifties housewife Miriam “Midge” Maisel, who discovers her talent for stand-up comedy after her husband – also an aspiring comedian – leaves her for his secretary.
In 2018, Brosnahan picked up the 2018 Emmy award for best actress in a comedy series on a night that saw The Marvelous Mrs Maisel take home a total of eight awards.
The SNL episode, which will air on 19 January, marks Brosnahan's SNL debut. She follows in the footsteps of previous hosts including Jonah Hill, Claire Foy, Ariana Grande and Steve Carrell.
It is the first SNL episode to air since Matt Damon hosted the episode on 15 December, which featured appearances from Robert De Niro, Alec Baldwin and Ben Stiller in the sketch It's a Wonderful Trump.
Brosnahan will be joined by a debut performance from musical guests Greta Van Fleet.
The Michigan based rock band are currently up for four Grammy awards at the 61st ceremony in February, including Best New Artist and Best Rock Album.
Their 2018 debut record Anthem of the Peaceful Army entered the Billboard rock chart at number one, and reached number 12 in the UK charts. However it received largely negative reviews from critics.
The next episode of SNL will air on NBC on 19 January
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