Chelsea finished fifth in the Premier League last season, 30 points adrift of Pep Guardiola's Manchester City, and behind Jose Mourinho's Manchester United, Mauricio Pochettino's Tottenham and Jurgen Klopp's Liverpool.
In a brief statement released on the club's official website, curiously only 61 words, the Blues wished the Italian the best for the future.
NAIJ.com previously reported that Chelsea announced the sacking of their manager Antonio Conte on their social media handle.
He told Italian radio station Radio Crc: "I am happy for Sarri because no one believed he could get there and instead here he is coaching Chelsea and it is a great victory for everyone, even for Napoli that was fundamental".
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Chelsea director Marina Granovskaia said: "Maurizio's Napoli side played some of the most exciting football in Europe, impressing with their attacking approach and dynamism".
Chelsea desperately need top quality in midfield after poor recent signings such as Tiemoue Bakayoko, Danny Drinkwater and Ross Barkley all failed to make an impact at Stamford Bridge last season.
The new Chelsea manager has already picked up Jorginho from his old club and the Sunday Mirror are reporting that Koulibaly is the next name on his shopping list. However, many media houses claimed Napoli used the midfielder to ease Sarri's move to Chelsea.
Sarri will be followed to West London by Napoli's Brazilian-born Italy global midfielder Jorginho, whose signing was also confirmed on Saturday by the Roman Abramovich-owned club.
Koulibaly's agent Bruno Satin was quoted by Talksport as saying both Norwich and the Saints were keen to sign his client, with Napoli putting the player up for sale. Their willingness to beat Manchester City's offer for Italy global midfielder Jorginho provided the belated breakthrough in talks.
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The midfielder, who revealed Juve's offer was the only one he had, said: "My story at Real was brilliant and I thank the fans". Pele made a similar decision in 1975 when he signed with the Cosmos, where he played out the rest of his career.