The 19-year-old has long been a target for the Blues and have met the Italian side’s asking price having previously had two offers under £10m turned down.
The Blues are set to beat late competition from French side Nice, who had hoped to hijack the transfer.
Chelsea are now discussing the fine details for the transfer and hope to arrange a medical for the box-to-box midfielder in the next 48 hours, with personal terms on a six-year deal verbally agreed on Monday night.
For Inter, the sale is understood to help fund the permanent signing of Romelu Lukaku - who is on a season-long loan at Chelsea, who there is an informal agreement between the two clubs over a second year at San Siro should circumstances fit.
The signing of Casadei is part of a succession plan for N’Golo Kante and Jorginho, who both have less than one year left on their current contracts.
It is also part of a drive by the new Boehly-Clearlake ownership group to further develop the club’s academy with director Neil Bath, taking it to the next level by signing the world’s best young talents.
Jose Feliciano of Clearlake Capital, who partly own Chelsea, was this week seen at Kingsmeadow alongside Bath and Thomas Tuchel watching the Under-21s’ shock 3-0 loss to Fulham.
Chelsea sign Carney Chukwuemeka
They watched on as Carney Chukwuemeka lined up for the first time in Chelsea colours after his £20m arrival from Aston Villa, featuring alongside Ben Chilwell, Trevoh Chalobah and Ethan Ampadu who were playing for match fitness.
Chelsea have now spent around £40m on academy stars including Casadei, Chukwuemeka, Omari Hutchinson from Arsenal, Leo Cardoso from West From and Southampton duo Tyler Dibling and Eddie Beach. At least one further signing at youth level being planned.
Including first-team signings, the summer spend is now over £180m with talks ongoing for Leicester defender Wesley Fofana, Everton forward Anthony Gordon and Barcelona duo Frenkie de Jong and Pierre Emerick Aubameyang.