Allan – who struggled for game time under Genarro Gattuso at Napoli – was thought to be a priority signing for Ancelotti in this window, with the Italian keen to be reunited with his former player.
Ancelotti has now got his wish, with Allan, a combative midfielder capped nine times by Brazil, joining Everton on a three-year contract for a reported fee of £22.2million (€25m) plus add-ons.
"It is a real pleasure to sign for Everton. I am immensely happy to be here," Allan told evertontv. "I hope, like I have done in my entire career, I contribute with my performances together with my team-mates and that I put in some great games, great performances and win important things.
"It is a club with a rich history in the Premier League, has real ambition and then there is Professor Ancelotti.
"He has done everything possible to bring me here.
"It is the size of the club and the name of the coach which means you don't think twice about coming to Everton."
Allan's arrival, along with the expected additions of James and Doucoure, has cast further doubt over the futures of some of Everton's squad, with the Toffees said to be open to offers for Theo Walcott, Bernard, Fabian Delph and Gylfi Sigurdsson – the club's record signing.
Muhamed Besic, Yannick Bolasie and Sandro Ramirez – who spent last season out on loan – are also for sale.
Everton begin their 2020-21 Premier League campaign at Tottenham on September 13.