The British funnywoman was snapped cuddling up to the host in a park in Los Angeles earlier this month (Sep12), and the pictures have been published in Britain's The Sun.
An onlooker tells the publication, "We were surprised to see them being so intimate. They looked very much into each other and had that besotted look in their eyes."
A source adds, "They're very happy together and love spending time with each other."
Tate, who has a daughter from a previous longterm relationship, has previously been linked to Take That star Jason Orange.