Thiago Silva completed his Chelsea medical in Milan on Thursday ahead of signing a free agent deal with the club.
The Brazilian centre-back resisted a last-ditch offer from PSG to make the switch to west London.
Silva, 35, is expected to sign a two-year deal with the Blues on Friday.
He will become Frank Lampard's fifth signing of a busy transfer window.
Malang Sarr, Ben Chilwell, Timo Werner and Hakim Ziyech have all arrived at Stamford Bridge this summer.
