The professional dancer lifted the glitterball trophy with BBC presenter Ore Oduba in December.
Oksana Platero - who danced with Judge Rinder - is also leaving the show, as is Natalie Lowe, who announced she was stepping down last month.
The new dancers are Amy Dowden, from South Wales, Australian Dianne Buswell and Nadiya Bychkova from Ukraine.
They will join the show alongside the remaining professional dancers when the contest returns to BBC One in September.
Joanne, who is currently starring in a tour of Thoroughly Modern Millie, said she would be sad to leave her Strictly "family" behind.
She said: "Being part of the Strictly experience has been one of the best things that has ever happened to me and I will miss the show so much.
"It's been a tough decision but I am looking forward to facing new challenges and focusing on my musical theatre career."
The dancer, who also won the 2015 Christmas special with Harry Judd, will take part in the first show of the series to perform with Ore.
Oksana, who only joined the show last year, said: "I had an unforgettable time working alongside such amazing dancers and an even better time with Judge Rinder.
"It was an opportunity of a lifetime and I will never forget it. Thank you so much for the memories."
New dancer Amy, from Caerphilly, is British national champion of Latin dancing and also one of the highest-ranking ballroom and Latin American professional dancers in the UK.
She said: "Becoming a professional dancer on Strictly Come Dancing has made my wildest dreams come true, it does not feel real!
"I have always been proud of my Welsh roots and feel so honoured to be the first Welsh professional dancer on the most loved show on TV."
Dianne is an Australian Open Champion and has taken part in Dancing with the Stars Australia and the Broadway production of Burn the Floor. Nadiya is a two-time world champion and European champion in ballroom and Latin "10" dance.
Joanne's brother Kevin is one of the returning professionals who will be matched with a celebrity at the start of the 2017 series. He joins male dancers Anton Du Beke, Brendan Cole, Neil Jones, Pasha Kovalev, Gorka Marquez, Giovanni Pernice, AJ Pritchard and Aljaz Skorjanec.
The other female dancers are Karen Clifton, Chloe Hewitt, Katya Jones, Oti Mabuse and Janette Manrara.
Follow us on Facebook, on Twitter @BBCNewsEnts, or on Instagram at bbcnewsents. If you have a story suggestion email entertainment.news@bbc.co.uk.
Current Strictly Come Dancing champion Joanne Clifton is stepping down to concentrate on musical theatre.