The hot new couple were virtually inseparable as they held hands during a stroll through the streets of Madrid yesterday (September 21).
Kate and her hunky model beau are in Spain for a Vanity Fair party — their first public appearance as a couple.
The 34-year-old actress – who separated from her film director husband Sam Mendes in March – was accompanied by Louis on the red carpet.
An onlooker said: “The chemistry between them looks fantastic. They seemed to want the world to know how great things are.”
Things are seemingly going so well between the pair – who started dating in July – Kate has reportedly asked Louis to live with her while she films new movie Contagion in Chicago, because she doesn’t want to have a long distance relationship.
A friend said: “They have discussed the idea of Louis going with her while she films so they won’t have to endure a long-distance relationship at such an early stage in what seems to be something pretty serious. Kate hasn’t been this happy in a very long time.”