The Brazilian joins compatriot Richarlison at Goodison Park, having penned a three-year contract on Merseyside.
Allan will wear the No.6 shirt at Everton, having donned the No.5 jersey during his time in Serie A with Napoli.
“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 teammates 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."
He added: "A strong part of my game is marking and the desire going in to win absolutely every ball," he explained.
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"I believe with my desire I can put in really good performances to win the fans over and I hope to win things as well. There will be a tremendous amount of dedication from me, a lot of dedication – a lot.
"I received a lot of messages from Everton fans and that made me really happy and confident in the work I can do here."
James Rodriguez is expected to follow Allan in joining Everton this weekend.
The Real Madrid playmaker has undergone his own medical ahead of completing a transfer to the Premier League side.
And it would mark another reunion for Ancelotti, who managed the Colombian at the Bernabeu as well as at Bayern Munich.
Watford's Abdoulaye Doucoure is also poised to bolster Everton's midfield further after a deal was agreed for him this week too.