The underwear model was spotted walking hand in hand with the 'Doctor Who' star at the Coachella Music and Arts Festival in California yesterday (18.04.10).
The pair reportedly met three months ago during a night out in Camden, London.
A source said: "They hit it off immediately and the chemistry between them was obvious from the start.
"It's early days but they are already talking about moving in together. They realised it was terrible timing with his debut in 'Doctor Who', so they went to great lengths to keep it secret.
"It wasn't even planned that they would reveal the relationship at Coachella - but Daisy has missed Matt while he was on the tour and they thought, 'What the hell?' After all, the reviews are in - it can't affect the show now."
Daisy and Matt were seen getting especially cosy at the festival and spent some time hanging out with socialites Peaches and Pixie Geldof and radio DJ Nick Grimshaw.
An onlooker said: "Matt looked smitten. He was so attentive to her and she couldn't stop smiling. She was hanging on to his every word.
"It was like the pair of them were in their own little bubble together. They were inseparable."
Despite attempts to keep their relationship quiet, Daisy hinted she was romantically involved with the 27-year-old actor - who has won rave reviews for his portrayal of The Doctor in the British sci-fi series.
Writing on twitter, Daisy said: "ok i am officially madly in love with doctor who... (sic)"
Matt too has hinted he has feelings for Daisy, saying last month: "Daisy Lowe's a pretty lady, someone lovely with a good heart who enjoys the thing I enjoy."