It's permission based... but if they already have them, removing that permission does not remove the signature. You would have to find an add-on that does that, or go through and manually edit each user. You will also need to make sure that any groups those users are members of do not have the signature permission set if you don't want them to create signatures.
Newly registered users on my site have this... they cannot create signatures... but I run a promotion that after a certain number of posts, it adds them to a group that allows them to.
There are two paid add-ons that appear to be able to do that.. but one I don't tend to recommend for personal reasons (and no, I won't discuss even in convo why).
The other one is
Description: Automatically remove user signature when they being remove some user groups. Options: Option to select user groups Enable/disable send a conversation to users Customize conversation creator Permissions: N/A