The Italian’s representatives spent the weekend in talks with Chelsea officials and the 41-year-old has been assured he is the man Roman Abramovich wants.
Di Matteo has agreed to accept the position in principle and the remaining contractual issues are expected to be ironed out this week.
The former West Brom manager returns from a family holiday on Wednesday.
It is thought Chelsea are likely to wait until Di Matteo is back in London before making an official announcement.
Di Matteo was appointed interim coach following the sacking of Andre Villas-Boas in March.
He led Chelsea to a historic Champions League triumph over Bayern Munich last month and also lifted the FA Cup as he lost just three out of 21 matches to restore much-needed pride to Stamford Bridge.
Di Matteo’s case was strengthened by the willingness of the senior players to see him handed the chance to build on last season’s triumphs.
One issue that remains unresolved, however, is the length of the contract.
Di Matteo had expressed a reluctance to accept a short-term deal, fearing it would affect his authority at the club and his ability to make long-term decisions.
It is now thought the most likely scenario will see both parties agree to a longer contract with a clause that would allow either to break it after 12 months.