The Ramsay Street pair have made no secret of their relationship on Twitter and Instagram in recent weeks, but have never publicly discussed their personal lives until now.
Speaking to TV Week, Milligan revealed that he has been dating Rosenow for the past five months.
The couple met for the first time late last year, when Rosenow, 22, joined the cast of Neighbours as Amber Turner.
Milligan, who plays Kyle Canning, explained: "She began in October and we started seeing each other in November.
"We went to Vanuatu together last week. It's all going really well."
Milligan, 25, has been part of the Neighbours cast on and off since 2008.
Digital Spy Soap Scoop video - press play below to watch Amie Parker-Williams reveal gossip on a huge week of Emmerdale, a romance twist in Coronation Street, and big danger for characters in EastEnders and Hollyoaks.