Mercedes announced earlier that Hamilton, McLaren's 2008 champion, had signed a three-year deal and will replace 43-year-old Schumacher in 2013.
The news may have signalled the end of Schumacher's unremarkable comeback but Mercedes refrained from saying the seven times world champion would be retiring as a result of the decision.
"I think Michael's going to take a few months to think about things and reflect on things, to decide what to do in the future," Brawn told Reuters in an interview at the team's factory in central England.
"Michael's been undecided for some time now in what to do," added the Briton.
"As Michael has been contemplating what he was going to do, then the opportunity to have Lewis join the team gradually increased, gradually grew to the point where we had to come to a conclusion.
"Michael's very happy for the team but I think he is going to spend the next few months thinking about what he is going to do.
"There are opportunities within the team, within Mercedes for Michael to stay involved in some capacity or other, and he's particularly interested in developing high performance cars, that sort of thing."
Sauber have a vacancy after Mexican Sergio Perez was announced as McLaren's replacement for 27-year-old Hamilton but it remains to be seen how much interest there is in signing a driver that some believe to be too old for the sport.
Brawn said the situation with Hamilton had evolved over several months after starting early in the year "in a relaxed way" with Schumacher informed at every stage.
The former Ferrari technical director, and title-winning Brawn GP principal, said Hamilton's arrival would put his team even more in the spotlight but was sure they would rise to the challenge.
"There's always huge pressure on us to perform and of course having a driver of Lewis's calibre in the team may intensify that pressure," he said.
"I think this is a team that has great potential, great facilities, great people.
"It's coming together now and I think Lewis will be able to both contribute to the end result as a driver but also contribute in giving the motivation and giving the input to the team, they're the things we need to do to produce a great car.
"So I believe we are going to produce great cars in the future."
Brawn said the belief that Mercedes could succeed was probably the most important factor in convincing Hamilton to make the change from a team that has nurtured him from his early teenage years.
"We want him to contribute much more than just driving a car, we want him to be a very integrated member of a team, we want him to contribute with the engineers, we want him to motivate the people, we want him to really become an intrinsic part of the team and I think that's what appealed to Lewis," he added.
Ferrari won five titles in a row with Schumacher in the early years of the century and Brawn won the drivers' and constructors' crowns in 2009. The team boss did not rule out replicating such success.
"I believe that we can go forward and with Lewis and Nico Rosberg we can enjoy the sort of success that Ferrari had in the 2000s," he said.