The 26-year old midfielder has penned a contract that will keep him at Parkhead until 2015 and amidst claims that Newcastle United were heavily interested, Brown insists he is happy in Glasgow.
"I could quite happily stay here for the remainder of my career," said Brown.
"I've got a great bunch of team-mates and this is a great place to be.
"I don't see it as a lack of ambition to go down to England. Some players have gone down there and gone missing."
Brown reportedly had some difficulty agreeing a deal with the Hoops but now it is done, he is delighted to be able to stay put.
"The difference was settled between the club and my agent," he added.
"I didn't get involved in any of that. I didn't do anything to make it happen, the club sorted it out. They were brilliant.
"I've said all along that Celtic's the club for me and I wanted to stay.
"I enjoy being here and it's a great way of life.
"Money's not always my biggest driving force - I've got to go where I enjoy playing football."