Di Matteo, 42, who took over from Andreas Villas-Boas in March on an interim basis, led Chelsea to the Champions League title and FA Cup glory last season.
The former Chelsea and Italy midfielder said: "I'm obviously delighted to have been appointed as manager and first-team coach.
"We all achieved incredible success last season that made history for this great club. Our aim is to continue building on that and I'm already planning and looking forward to the squad's return for pre-season."
"Roberto's quality was clear for all to see when he galvanised the squad last season and helped the club make history, and the owner and board are very pleased he will be continuing his good work," said Chelsea chief executive Ron Gourlay.
No London club had ever won the European Cup or Champions League until Chelsea beat Bayern Munich in the German club's home ground in May.
Source: AFP
Source: AFP