The pair were spotted for the first time getting cosy on a dinner date in Malibu.
A source told PEOPLE: ‘Chris and Dakota arrived together in Chris’ car. They met up with friends and had a fun night. They both seemed very happy. They were flirty, and also left the restaurant together.’
Dakota, 28 and Chris, 40 first sparked relationship rumours in October last year when the two were seen on a sushi date in Los Angeles.
Following the date, Dakota was then later snapped by a fan at a Coldplay show in Argentina.
Chris was previously married to Gwenyth Paltrow for 10 years before divorcing in March 2014 while Dakota's last relationship was with American-Welsh rocker, Matthew Hitt until they reportedly went their separate ways in June 2016.