There are several reasons why your boss wouldn't want you to tell employees:
Informing everyone orderly
If your position in your current job is above the lowest hierarchy and your departure impacts a lot of people, your boss probably wants to tell everyone in an orderly fashion in a meeting or email to all employees. This also puts him in a position of control - he tells everyone of your departure in contrast to you telling everyone that you are leaving, whether or not he likes it.
Plan of action
Your boss now has to come up with a plan on how work will be organized, who adopts your tasks, whether to hire someone else and so on. Forming this plan will take some time, hiring someone else even longer.
This directly relates to the meeting / email, in which he will not only inform everyone of your departure, but of his plan as well. He will probably delay the announcement until he has at least a rough plan.
If he cannot come up with any plan at all, he will try to delay the announcement as long as possible...
Stop the rumor mill
Have you heard yet? Alice quit her job yesterday. No way! I heard she was fired. Should we be worried about loosing our own jobs?
If you tell only a few employees that you're leaving, this information will spread irregularily, deformed and misinterpreted, giving way to rumors. informing everyone at once gives this kind of rumor no chance.
Keeping motivation up
Sometimes an employee might look at drastical changes in the future and ask themselves "Why am I still doing this? Will what I'm doing now be useless and obsolete in 2 weeks? Why do anything at all before the new guy is hired / the new plan is in action?"
In my experience, the changes really have to be quite drastic, so I'm not sure this applies in your case. But if it applies, from your bosses point of view, the best he can do is let his employees work as before instead of demotivating them.
Keep other employees from quitting
There are always some people who are not content with their job, their colleagues, the workplace or company. The sooner those people know that you are leaving, the more time they have to talk with you about how unhappy they are and how they want to leave as well. Especially if you already have a new job and are (understandably) excited to start at the new company. This may strengthen their resolve to leave as well, resulting in a wave of cancellations.