Ball stood in for Claudia Winkleman last year, who missed the BBC Two series due to maternity leave.
The former Live & Kicking presenter will now replace Winkleman permanently when the show returns in September.
Meanwhile, Winkleman is expected to retain her spot on the Sunday results show, which she co-hosts with Tess Daly.
Speaking to Digital Spy earlier this year about her move away from It Takes Two, Winkleman said: "I'm not going to do the daily show. That is now Zoe's and she is brilliant and far better at it than I ever could be."
Strictly returns to BBC One this autumn and star names such as Ronnie O'Sullivan, Charlie Brooks, Sian Williams and Michael Vaughan are being tipped to take part.
