AceShowbiz -

Keeping mum about their much publicized romance, Taylor Swift and Calvin Harris are no longer shy to put a united front in public. The lovebirds were caught on camera holding hands as they were having dinner at Giorgio Baldi restaurant in Santa Monica, California, on Tuesday evening, May 12.

Swift, 25, wore an all-black ensemble with matching clutch during the outing and she finished off her look with bold red lipstick. As for Harris, 31, he opted to wear a white shirt under his trouser which he combined with black pants and sneakers. The duo was spotted sporting smiles on their faces.

"They were very close together, leaning in to speak to each other and laughing a lot," an onlooker informed PEOPLE. "Taylor looked gorgeous. It was a very sexy but classy look. She was glowing, she seemed incredibly happy but also very at ease with Calvin." The onlooker added, "They were dressed up and enjoying themselves, talking and laughing the entire time."

Swift and Harris have been romantically linked since March after they were spotted getting cozy at Kenny Chesney's concert. Last week the songstress was photographed supporting Harris' performance at Wango Tango festival.