The Congo born Portugal international, 25, has a four-year deal which has cost Chelsea £16.2m.
The move spells the end for Juliano Belletti who signed from Barcelona last year.
The Brazilian lost his place and moved further down the pecking order with Avram Grant preferring to use midfielder Michael Essien instead of him or Paulo Ferreira.
However Ferreira had recently signed a new five-year deal and will provide cover for Bosingwa who won the Champions League in 2004 with Porto under Jose Mourinho.
He will undergo a medical today and will join the squad fopr their pre-season tour of China in July.