Ms May, who a few weeks ago commented she was “cheering on Debbie McGee”, took to Twitter.
Ms Sturgeon also expressed her joy at McFadden’s victory, tweeting: “Brilliant! Well done to the lovely @mrjoemcfadden - well deserved @bbcstrictly champion”.
Former politician and one of last year’s Strictly Come Dancing contestants, Ed Balls, said the couple were worthy champions.
Last year Balls was partnered with this year’s winning professional dancer, Katya Jones.
He tweeted: “I said last year that @Mrs_katjones is a genius and would go on to be a Knock-Out Strictly Superstar - And here we are! Huge congratulations to Katya and the brilliant @mrjoemcfadden - such worthy @bbcstrictly Champions! I’m so pleased for Joe and so so proud of Katya !”
Last year’s winner Ore Oduba also congratulated the winning pair, describing the final as “amazing”.
Strictly’s head judge Shirley Ballas said it was a “deserved” win as she tweeted a photograph of herself alongside them, writing: “So deserved! Massive congratulations to @mrjoemcfadden and @Mrs_katjones @bbcstrictly 2017 winners! ?? #Strictly.”
The Reverend Richard Coles, who was one of this year’s celebrity contestants on Strictly, said he had the pair down as winner’s from day one.
He tweeted: “I know it’s annoying when people say this but I had Joe and Katia to win from day one #Strictly”.
McFadden and Jones beat the three other couples competing in the final to be named this year’s winners.