The 52-year-old singer was firs photographed leaving a cinema in New York with Zaibat last week, whom she is thought to have been dating for the past 'few months'.
A source told gossip website X17Online.com: 'They've been seeing each other for a few months but really keeping it on the down low.
'Madonna did not want this getting out before she had time to see if things were really going to work out between her and Brahim or not.
'Things have been going well so she was about to go public with the relationship anyway.'
Wrapped up: While her boyfriend hid, Madonna appeared not to mind the attention
While Zaibat's age has not yet been revealed, it is thought the dancer is in his twenties. Madonna's former boyfriend Jesus Luz is currently 24.
The new pictures come after it had been claimed Madonna was dating another of her backup dancers with the same name - Brahim Rachiki.
It is claimed Madonna was furious after it was reported she was dating Rachiki, and decided to set the record straight about the identity of her new boyfriend.
Madonna and Zaibat were first seen together in New York nightclub SL, where they apparently started cuddling and kissing in front of clubgoers.