The 25-year-old singer and 31-year-old Scottish DJ were all smiles as they headed to Giorgio Baldi restaurant for dinner Tuesday.
Swift and Harris were first linked after they were photographed grocery shopping together in March. The alleged couple were seen holding hands weeks later at a Haim concert, and the DJ met the pop star's two famous cats in late April.
Swift previously dated actor Jake Gyllenhaal and fellow musicians John Mayer and Harry Styles, while Harris was involved with singer Rita Ora. Ora later told Cosmopolitan magazine Harris was "the right guy at the wrong time."