LeBlanc, 48, is said to be "besotted" with Aurora Mulligan, who works as an assistant producer on TV show "Top Gear", which the actor co-hosts.
The pair went public with their romance as they enjoyed a date at a horse racing event in West Sussex, South England, and fellow racegoers say they couldn't keep their hands off each other.
"Matt and Aurora were inseparable throughout the whole day. They were very tactile and Matt seemed to be very taken by Aurora as he laughed chatted intimately with her. Aurora just kept laughing at all his jokes and is clearly besotted with the American superstar," a source said.
LeBlanc and Aurora were first linked with each other earlier this year.
LeBlanc, who co-hosts the BBC show alongside Chris Evans, was previously married to model Melissa McKnight and they have a 12-year-old daughter, Marina, together.
He also dated actress Andrea Anders for nine years, before splitting in October 2015.