Photographs of the pair on holiday in Santa Monica, California were printed in The Sun, and the actress and TV presenter are said to have been dating discreetly for most of the year.
"We were surprised to see them being so intimate. They looked very much into each other and had that besotted look in their eyes," claimed an eyewitness.
A friend is additionally quoted as saying that Tate and Chiles are "very happy together and love spending time with each other".
Tate, who has a 9-year-old daughter from a previous relationship, reportedly started a relationship with Take That singer Jason Orange in late 2011. They are believed to have broken up in February of this year.
She is now a series regular on NBC comedy The Office.
Ex-Daybreak presenter Chiles divorced Woman's Hour presenter Jane Garvey in 2009. The former couple have two daughters.