Napoli confirmed Gattuso’s appointment on their verified Twitter handle on Wednesday.
Ancelotti was relieved of his duties as Napoli coach after 19 months in charge.
Napoli announced the decision to dismiss Ancelotti an hour after he led the club to the knockout stages of the Champions League with a 4-0 home win against Genk.
The win ended a nine-match run in all competitions without a victory.
According to Sky in Italy on Tuesday, Gattuso was the leading candidate to take over at Napoli.
Napoli, who face Parma in their next game on Saturday, are currently seventh in Serie A.
Under Ancelotti’s guidance, Gattuso won Serie A, Coppa Italia, Supercoppa Italiana, UEFA Champions League, UEFA Super Cup and FIFA Club World Cup.
Commenting on his relationship with the departed Ancelotti, during his unveiling ceremony on Wednesday, Gattuso described him as a father figure.
“Ancelotti is like a father to me. He’s always been close to me and supported me. He’s won it all and I still have a lot to prove.”
And on the huge task before him, Gattuso said: “The aim is to recoup points and get back into the Champions League positions. We need to work hard, win back points and come through this tricky period.
“It’s embarrassing to see Napoli where we currently are in the table. This team has what it takes to finish in the top four. The team is aware of the difficult situation and wants to do well. I’ve been encouraged. I fear nothing. I know I’m going to be working with experienced people. I hope to get results.”
Speaking further, Gattuso added: “The perception of Napoli abroad is much bigger than you can imagine.
“We need to get down to it and win our next two games before the break.
“All of the players are in my plans. Insigne is a club asset, like all the others.
“We need to make sure our performances bring some enthusiasm back to the city.”
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