Conte regularly questioned the club's ambition and dealings in the transfer window and departs after failing to guide the Blues into next season's Champions League.
Assuming both deals get over the line, Jorginho and Sarri should be at Chelsea by this weekend at a total cost of around €65m to secure both signings.
The Blues missed out on a place in the Champions League despite starting the 2017-18 season as Premier League title holders following Conte's successful debut campaign in England.
Conte began his career at Lecce, playing as a midfielder.
The former Italy national coach returned to take training this week but the writing was on the wall and the drawn-out process was reportedly due to how much compensation the club should pay Napoli for Sarri.
Chelsea and Napoli have agreed a deal which features an initial £50m fee with £7m in bonuses. Their willingness to beat Manchester City's offer for Italy global midfielder Jorginho provided the belated breakthrough in talks.
Chelsea sack Antonio Conte
Conte departs a year before his contract was due to expire and will now be in line for £9million in compensation. Despite Chelsea being linked with several managers, Conte refused to step down from his post.
Goal understands Chelsea will pay £57m (€65m/$86m) for the player, with Jorginho having signed a five-year contract with the club, where he will earn £102k per week.
"He has demonstrated his quality working under Maurizio Sarri and we are convinced his signing will help bring further success to Stamford Bridge".
Sarri, who has risen from the amateur ranks of Italian football, will be working outside of his native country for the first time.
Conte has been sacked after two years at Chelsea.
Winning trophies didn't save Conte being shown the Stamford Bridge exit door as he was dismissed after guiding Chelsea to the FA Cup in May.
It was on the cards long before last season's FA Cup triumph, which came less than 12 months after he won the Premier League.