The contract, worth a six-figure annual fee, began this month.
It is the first time Virgin Trains has consolidated its PR and social briefs into one account, Kaper said in a statement.
Incumbent agencies Hope&Glory and Nonsense, which handled PR and social respectively, declined to re-pitch for the business.
Hope&Glory managing partner Jo Carr said: "We politely declined the opportunity to re-pitch. While we loved working with Virgin Trains, we agreed it's time to part company as their needs changed."
Kaper's remit includes consumer PR campaigns, social content and brand engagement. The account will be led by Kaper founder Chris McCafferty and deputy MD Nicola Dodd.
McCafferty said: "Virgin Trains is one of the UK's best-loved brands with a record of bold creativity. We're the lucky agency that gets to join the Virgin Trains family and deliver more brave, standout work."