On Friday, the country star posted an adorable photo of the new duo cuddling on a couch.
"The snuggle is real," she captioned the Instagram picture.
PEOPLE confirmed on Tuesday that Lambert, 32, and East, 27, whose real name is Michael Cameron Anderson, are dating.
The Nashville-based musician is currently touring for his 2015 album, Delilah.
Lambert and fellow country star Blake Shelton split in July after four years of marriage.
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"I'm still processing everything and figuring out where to go and what happened," Lambert shared in the January issue of Cosmopolitan.
While Lambert just made her new relationship official this week, Shelton has been seeing fellow Voice judge Gwen Stefani since November.
On Monday, Shelton, 39, and Stefani, 46, took a tour of a winery in California.