The Italian guided the west London club to FA Cup and Champions League success after taking over from Andre Villas-Boas as first-team coach on an interim basis in March.
The 42-year-old 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."
The Italian returned to Stamford Bridge following his holiday to finalise a two-year contract.
Chief executive Ron Gourlay said: "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.
"We all believed he was a young coach with much to offer when we first asked him to take charge of team affairs in March and the manner in which he worked with us, the players and all the staff, and the success that followed, made him the clear choice when it came to selecting the person to take us forward in the seasons to come.
'"We will be working closely with Roberto in the weeks ahead, some exciting signings have already been made and Roberto has had input into those.
"Although he has set the bar very high in the short time he has been in charge, we know that Roberto is the right man to lead Chelsea onto further success."