It's can be very difficult to contain your excitement when you find out that you're going to have a baby. There are certain instances during pregnancy when you must exercise restraint and control the flow of information as if it were a matter of national security. The announcement is one of them.
I personally wanted to run out and tell everyone as soon as the pee test was dry, but announcing a pregnancy can be considerably more complicated than most men would ever expect. There are numerous considerations ranging from who to tell, in what order to tell them and how to do it. It is laughably easy to offend someone by not telling them soon enough or letting the news get back to them second hand.
I will get more in depth in future posts about making the big announcement, but my key piece of advice is to wait three months before announcing a pregnancy. I know this sounds like a long time to wait, but speaking from the perspective of someone who has had to go back and “untell” a bunch of people after a miscarriage, it's better off. The rate of miscarriage drops significantly after three months, so it's a good rule of thumb to follow for breaking the news.
It may become a moot point if her morning sickness or general symptoms raise suspicion in people, but still try to keep things under wraps as much as possible.