Villas-Boas, whose signing had been rumoured earlier in the week, is thought to have been given a two-year contract with an option for a third.
The 33-year-old resigned from his coaching position at home team Porto yesterday, which seemed to confirm speculation of a return to Stamford Bridge.
Villas-Boas had worked as a tactician under Jose Mourinho during his Blues managerial stint, as well as at Porto and Inter Milan.
He previously managed at Academica de Coimbra in 2009 before taking over at Porto the following year.
“Andre was the outstanding candidate for the job,” said a statement from Chelsea. “He is one of the most talented young managers in football today and has already achieved much in a relatively short space of time.
“His ambition, drive and determination matches that of Chelsea and we are confident Andre's leadership of the team will result in greater successes in major domestic and European competitions.
“Andre will bring his coaching experience back to a club he is already very familiar with, having previously worked here for three years. He has always been highly regarded at Chelsea and everyone here looks forward to welcoming him back and working with him.”