The Partenopei, who finished second in Serie A this season with a record points tally, chose to stop talks with Sarri over a new contract.
According to the Guardian, Ancelotti is expected to earn a salary of €6m (£5.2m) per season.
Contact between De Laurentiis and the former AC Milan and Real Madrid coach has been ongoing for weeks amid the indecision of Sarri, who has a contract with Napoli until 2020.
The Italian, who had also been tipped for the Azzurri national team job before Roberto Mancini was appointed, is replacing Maurizio Sarri at Napoli.
And on Wednesday evening it was confirmed that Carlo Ancelotti will take the reins at Napoli following Sarri's departure.
Meanwhile, he has won league titles in Italy, France, England and Germany.
And the Serie A side are prepared to let the deal go through and will also allow Sarri's £7m release clause to be waived if one condition is met. He returns nine years later to Serie A where he was named coach of the year in 2001 and 2004 at Milan, the club where he won eight championships.
Napoli have confirmed Maurizio Sarri has stepped down as manager of the club amid reports linking him to the Chelsea job.
Earlier reports had suggested Zenit offered Sarri £3.5m a season to come to Russian Federation following the departure of Roberto Mancini.