In 2006, she co-starred as Isolde in the romantic drama Tristan and Isolde.
Myles appeared as Madame de Pompadour in the 2006 Doctor Who episode "The Girl in the Fireplace".
They has been dating for the last couple of months.
In 2003, she starred in the thriller Out of Bounds and played Lady Penelope in Thunderbirds.
He has already had three romances with colleagues since taking over the controls of the Tardis in 2005. Miss Moffett, a 23-year-old single mother, played the Doctor's daughter Jenny in the current series.
To complete the Who connection she is the daughter of Peter Davison, who played the Time Lord between 19, and American actress Sandra Dickinson.
Low-key: David Tennant and his new girlfriend Georgia Moffett leave his north London home on Saturday morning Tennant, 37, and Miss Moffett were photographed leaving his North London houseafter spending the night there on Friday, before meeting on Saturday night at her West London home. He has a record for romancing his leading ladies and members of the film crew and his relationship with Miss Moffett is merely the latest in line of on-set liaisons on Doctor Who.
In April, he was reported to be dating second assistant director Jennie Fava, who moved to Cardiff to help film the latest series of the hit BBC1 programme which has been running since 1963.