should I keep myself quiet and wait for them to inform the team?
Whenever I resign from a job, I always tell my boss first.
Then I ask if he or she will be telling others, and when. Since I am in management, I always request the courtesy of telling my team directly - that has always been granted.
Often, I am asked to wait a few days while my boss notifies others in the management chain, and occasionally tries to convince me to stay. I always agree to wait a few days, although I don't accept a counter-offer.
Within a few days I start telling others, if they haven't heard already.
In short, talk with you boss and arrange a time in the near future so that everyone will know about your departure one way or the other.