Ball took charge of the first team for three matches following the dismissal of Paolo Di Canio, but has now been replaced by Gus Poyet, who has signed a two-year deal to become the head coach at the club.
"I would like to thank Kevin, along with Robbie Stockdale, Mark Prudhoe and Scott Pearce, who stepped in at a moment's notice in what was a very difficult situation," Ellis told the club's official website.
"Without any hesitation, they gave 100% to the cause. As usual, Kevin gave his all for the benefit of our club and we are very grateful to him for his ongoing commitment."
Poyet heads into his new role with Sunderland at the bottom of the Premier League table.