The Oscar winner stepped out with her beau on Tuesday for a romantic date night here and they walked arm-in-arm as they entered a restaurant, people.com.
The outing came only hours after Berry posted on Instagram a photograph with the British-born producer.
"My Balance," she captioned the image in which they are seen in a cosy embrace.
Alex also shared the same picture and he gave it the same caption.
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This marks Berry's first relationship since separating from French actor Olivier Martinez and finalizing their divorce in December 2016.
The actress has a 9-year-old daughter Nahla Ariela with former boyfriend Gabriel Aubry and 3-year-old son Maceo Robert with Martinez. She was also previously married to baseball player David Justice from 1993 to 1996 and musician Eric Benet from 2001 to 2003.