Reports about the Oscar-winner's blossoming romance first emerged at the start of the month when Kate, 34, and Louis where seen exercising together in New York.
And as the couple enjoyed a night out together in London's West End, it was apparent that the relationship is going from strength to strength.
Dressed in a little black dress, and with her hair held in a ponytail, smiling Kate looked smitten with Louis, also 34, on their first public outing.
British model Louis, who has starred in high-profile campaigns for Burberry, Paco Rabanne and Paul Smith, and Kate are said to have become inseparable since being introduced by mutual friends at a party.
Their romance comes five months after the Revolutionary Road actress and her estranged husband, 45-year-old director Sam, announced they were separating after nearly seven years of marriage.
She was also married to Jim Threapleton from 1998 until 2001, with whom she had a daughter, Mia Honey, now nine. Kate and Sam are parents to six-year-old Joe.