The model and The Last Shadow Puppets star, 23, have been linked since they were spotted at London clubs Bungalow 8 and Punk last month.
But they finally went public when they started snogging on the grass at London's Hamstead Heath.
'Miles and Agy get on like a house on fire and have a proper laugh,' a source tells The Sun.
'Miles bowled her off her feet. His pals ask about her but all he says is things are "boss". They have passed the three-week mark now.
'He lives in Liverpool but has been in the Big Smoke charming the pants off her. She’s very down to earth. That’s her appeal.'
Agyness, 26, recently split from rocker Alex Greenwald.
She was previously engaged to The Strokes guitarist Albert Hammond Jr.
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