The corporation announces the news tonight as the second series completes its television airing on BBC One.
In addition to the third series - likely to run for another four episodes, although this has not yet been confirmed - BBC bosses have commissioned a Christmas special, which will mix new sketches with highlights from the nine episodes to date.
Made by BBC Studios, Famalam stars Samson Kayo, Vivienne Acheampong, John MacMillan, Roxy Sternberg, Tom Moutchi, Gbemisola Ikumelo and Akemnji Ndifornyen. Regular support comes from actor and stand-up comedian Kieran Hodgson, amongst others.
Ndifornyen, who is also one of the programme's main writers, as well as the producer and one of its composers, quipped today: "Going for a three-peat! Excited to bring this beast back for another side splitting run! Third time's the charm!"
Shane Allen, Controller of Comedy Commissioning, says: "Famalam goes from strength to strength in keeping the modern day sketch show flag flying high with its super-talented cast, pin sharp social commentary and ideas that poke fun in all directions."
Earlier this year Akemnji Ndifornyen won a BAFTA Craft Award for Breakthrough Talent, and cast member Samson Kayo has received both BAFTA and RTS Award nominations. Series 1 was nominated for a Screenwriters Award in 2018 and the show has recently been nominated in the best comedy series category at the Edinburgh TV Awards 2019.
All nine episodes are currently available to watch on BBC iPlayer.
Transmission details for Series 3 and the Christmas special will be confirmed in due course.
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