The 41-year-old led Milan to fifth place in Serie A last season, but departed in the summer with two years still to run on his contract. Gattuso spent 13 seasons with Milan as a player – several of them under Ancelotti.
On joining, 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.
‘The team is aware of the difficult situation and wants to do well. I’ve been encouraged.’
Gattuso is expected to bring in his close friend and former teammate Luigi Riccio as his assistant at Napoli.
The legendary midfielder also revealed that Ancelotti spoke to him on the phone, wishing him well in his new role.
‘Carlo 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.’
Ancelotti has been linked with the vacancies at Arsenal and Everton in recent days. Gattuso’s reign begins with a home game against Parma on Saturday, before a trip to Sassuolo on 22 December