The 33-year-old has signed a three-year contract with the Stamford Bridge club after resigning from his post with Porto on Tuesday.
A statement on the Chelsea website read: "Andre was the outstanding candidate for the job. He is one of the most talented young managers in football today and has already achieved much in a relatively short space of time."
Chelsea confirmed Villas-Boas will take up his post "immediately".
The Blues were impressed by what their former backroom scout had achieved during his first managerial post.
"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