According to The Sun, the comedian fell for Halliwell at rehearsals for the London 2012 Olympic Games closing ceremony - where they were both performing.
It is thought Brand dumped Brewster earlier this month in order to pursue a relationship with Ginger Spice, with pals close to the 37-year old revealing he is 'smitten' and that things are "very serious" between the pair.
One of Russell's friends told the tabloid: "Things are getting very serious between them — they’re a proper couple now. They had met several times in the past, but really got to know each other during the Olympics.
“People thought Russell was joking at the time, when he said he had a crush on Geri all over again, but it was true."
The source added: “They just clicked — they have so much in common. He is spending so much more time in London just to be with her.”
Another close pal of Russell's said: “He ended his relationship with Isabella Brewster, and is now dating Geri properly.
“They’ve exactly the same sense of humour and are serious about clean living.”
They have apparently already enjoyed a string of dates, including a tour of Hampton Court Palace with Geri's six-year old daughter Bluebell over the weekend.
Brand and Halliwell were said to have been laughing and joking while holding hands on the date, with onlooker Greg Oram telling The Sun: "I thought it was the most random thing ever to see Russell Brand of all people in a place like that — until my wife pointed out he was with a Spice Girl.
"They seemed like they were having a really great time, holding hands and chatting — it was 100 per cent obvious they were a couple.
“Geri was holding his hand the same way I hold my wife’s. It was so cute.”
Following his performance at the Olympics closing ceremony,Katy Perry's ex-hubby hinted at his feelings for Geri, with Brand stating: “I’ve got a crush on Geri Halliwell — everything in the world is how it should be.”