The Serie A club had not won in nine games in all competitions until Tuesday’s 4-0 success at home to Genk.
Ancelotti was in his second season in charge of Napoli but they sit seventh in the league after that poor run.
They are the only team to beat Liverpool in 90 minutes this season, defeating the Reds 2-0 in September.
Last month the manager and Napoli players were in a high-profile dispute with president Aurelio de Laurentiis.
De Laurentiis ordered the team to attend a week-long training camp but Ancelotti and his players all returned home.
He is one of only three managers to win three European Cups/Champions Leagues – along with Liverpool legend Bob Paisley and current Real Madrid boss Zinedine Zidane.
He did not appear to know an announcement was imminent after the win over Genk, when he said:
“I’ll speak to president De Laurentiis tomorrow and we’ll make the best decision for Napoli.
“As far as I’m concerned, with certain players coming back and the right conditions in place, this team can still target fourth place.
“The win tonight is a weight off our shoulders and can give the players a big boost for the future.”
But a tweet later that evening simply read:
“SSC Napoli has taken the decision to part ways with first-team coach Carlo Ancelotti.
“The friendship and mutual respect between the club, president Aurelio de Laurentiis and Carlo Ancelotti remain intact.”
Reports in the Italian media suggest that Gennaro Gattuso, sacked by AC Milan at the end of last season, has been lined up as Ancelotti’s replacement.