The highly rated full-back has signed a five-year deal on the south coast with the Saints paying a fee of £5million.
Livramento, who was named the Blues' academy player of the year last season, is one of a number of Chelsea youngsters to leave this summer.
Tariq Lamptey left the club ahead of last season and, before injury, showed what is possible away from Stamford Bridge by shining at Brighton.
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