After months of speculation about his future, Hamilton decided to leave McLaren and switch to Mercedes, a move that was announced on Friday last week.
Hamilton will replace Michael Schumacher and partner Nico Rosberg at the team.
Brawn admitted it was "pleasant" that Hamilton just wanted the same chances as the German driver when he joins next year.
"Lewis never asked for any priority at all, he just asked for equality," Brawn told AUTOSPORT.
"He was pleasant in that he had no desires to have any special treatment or any unique facilities. Lewis just expects to have an equal opportunity in the team, as we would like to do as well.
"The conversation was relatively short in that area and I was impressed that he was positive enough to take that view and not attempt to protect some sort of position which would have been quite difficult for the team to accept.
"We never got into a discussion because Lewis didn't raise it. And if he had raised it, we probably wouldn't have wanted to do it."
Brawn reckons there will be no frictions between Rosberg and Hamilton, who remain friends having been team-mates when they raced in karting.
"They are good ex-colleagues and friends and I know that they travel to races together often," Brawn added.
"I don't expect them to have any issues at all. I've kept Nico informed as things have progressed and he is quite excited actually to have Lewis joining the team.
"I see that as a positive. We'll have the normal drivers trying to beat each other issues and that's what they have to be because we don't want a driver who doesn't want to beat his team-mate. But it is important that it's done in the right way. I think that will be a very good combination."
The team boss has little doubt that Hamilton will adapt to life at Mercedes, despite having spent his entire Formula 1 career at McLaren.
"I'm sure he's had a great deal of support at McLaren but you never know until you start working with anyone really," said Brawn when asked if Mercedes could bring the best out of Hamilton.
"We have our views on how we should approach things and it seems to align with Lewis's views of how he'd like to approach things and I'm optimistic that it's going to be a strong team, not just with me but the rest of the company."