Swaby joins the club on a permanent deal from AC Milan for an undisclosed fee, signing a contract until June 2027.
The 28-year-old brings a vast wealth of experience to South London, having played top-flight football in the United States, France and Italy, as well as having won 37 caps for Jamaica.
The centre-back began her career at the Boston College Eagles, before moving to Icelandic team Knattspyrnufélag Fjarðabyggðar (KFF).
She then made the move to Italy, where she featured regularly for AS Roma between 2018 and 2022.
During her time in the Italian capital, Swaby played a key role in helping the club secure their first-ever major trophy – the Coppa Italia – in 2021.