The 54-year-old former Juventus and Bari midfielder will be assisted by Alex Dyer and has agreed a three-year contract at Rugby Park. Alessio was a coach at Napoli before going on to work as Antonio Conte's No 2 at Juventus, Chelsea and Italy.
Killie director Billy Bowie told the club website: “On behalf of the board, I’m delighted to name Angelo as the new manager of Kilmarnock FC. We were extremely impressed by the calibre of the candidates but Angelo’s knowledge and passion for the role really shone through.
“This is a hugely exciting period for Kilmarnock, as we celebrate the club’s 150th anniversary and play European football for the first time in 18 years, and we’re looking forward to this new chapter with Angelo at the helm.”