The former Milan boss has been given a six-month contract, with provision for an additional year if certain results are achieved, such as qualifying for the Champions League.
Gattuso took training on Tuesday, less than 24 hours after his former AC Milan mentor departed.
The club have struggled in recent weeks and they are winless in seven Serie A games in succession, sitting seventh in the table and 17 points off leaders Juventus.
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 played under Ancelotti at AC Milan and said:
“He 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.”