The couple, who were first rumoured to be dating last month, were pictured leaving Nick Grimshaw's 30th birthday party on Friday.
Holding hands and smiling shyly, the pair seemed comfortable to be photographed together for the first time.
It is thought that supermodel Kate Moss played matchmaker, introducing the actress, 37, to the football agent just recently.
A friend of the couple told The Sun: "This is the real deal. Dave and Liv are madly in love.
"They mix in the same circles because Dave hangs out a lot with a group that includes Kate and Stella McCartney."
Liv Tyler split from her British rocker husband of five years Royston Langdon in 2008. They have a son together, Milo William Langdon, who was born in 2004.
Dave was last linked to Rita Ora and Kelly Brook. He was previously married to Davina Taylor, with who he has son.