Antonio Rudiger has made 72 appearances in two seasons for Roma.
The 24-year-old Germany centre-back is set to undergo a medical on Monday and finalise personal terms on a five-year contract.
Sky in Italy are reporting an agreement of £29m up-front with a further £4.4m in add-ons has been sealed between the clubs.
Antonio Rudiger is a Germany international centre-back with 16 caps
Sky sources reported earlier on Friday that the Blues had begun talks with Roma to sign the centre-half, who joined the Serie A side from Stuttgart for £7.6m last summer.
Chelsea boss Antonio Conte has been keen to sign a centre-back this summer following the sale of Nathan Ake to Bournemouth and the departure of long-term club captain John Terry.
Not the top signing but still an improvement for the team, I think he will adapt very fast to the PL.
Agreed with Golazo on the fact he should adapt to PL quickly. Also, considering the fact that Chelsea got so many CB in its base formation and the fact Chelsea will get in CL next season, adding depth in this position is imperative. Wouldn't be suprise to see him and Zouma get plenty of playing time thanks to that and maybe even having him start over Cahill if he show sign of being an improvement.