Grand Tour star Hammond, 56, was seen and pictured by The Sun holding hands with therapist Keira Glen, 53, during a recent outing in Abergavenny.
The couple were photographed outside a Waitrose supermarket, where Mr Hammond was seen loading shopping—including two green bags and a box of Guinness—into the boot of a classic Morgan sports car.
Earlier that day, they attended a classic car show at St Michael’s Hospice in Hereford.
The relationship comes after his 23-year marriage to Mindy Etheridge ended in January last year.
A friend told The Sun: “Richard is having fun and appreciates he’s lucky to have someone he shares such a spark with.
“He wasn’t expecting to get into a relationship so quickly, but he’s not complaining.
“It’s early days, but they’re happy to see where it goes with no pressure.”
Mr Hammond shares two daughters, Izzy, 25, and Willow, 22, with his ex-wife.
Ms Glen also has two daughters, aged 26 and 24.