Password policy change

In the past we pretty much allowed very simple policy with passwords. With people accessing the cloud more and people logging in remotely to our site we need to make passwords a little more difficult.  My question is if I changed the password policy will this immediately affect all users.  Frankly I only want to have them change their password to a stronger password when their old password expires.  This will reduce the support that will be needed.  I mean if I change the policy and suddenly everybody needs to change their password on the same day I'm sure I'll get support calls and grumbling etc.

So to repeat my question if I change the password policy so that people need to put in more complex passwords will this affect everyone immediately or will it only affects them the next time the password expires, which we have set 120 days.

Thank you