The Coldplay frontman was first linked to the Peaky Blinders star in August (15), and the new couple showed off their romance in public over the weekend (17-18Oct15) by locking lips in a street.
They also joked around by playfully dancing the tango down the road, and in images Chris can be seen hysterically laughing.
Chris, 38, and Annabelle, 31, first sparked dating rumours when they were pictured heading into a New York hotel together.
At the time, a source told Usmagazine.com the couple had been dating "for about a month", adding, "He visited her while she was filming (Peaky Blinders) in Vancouver and really likes her."
The singer split from his wife Gwyneth Paltrow last year (14) after more than a decade of marriage. He was later linked to The Hunger Games star Jennifer Lawrence.