I have a 1 year lease in San Francisco and I gave a 30 day notice of intent to vacate to my property manager by e-mail on 5/11/12 stating that I intended to vacate on or about 6/30/11 but I said I may need to extend the move out date a bit and that I understood from our discussions that this should not be a problem. My communication of my intent to vacate was sent by e-mail and I did not provide any special form for this notification. My lease agreement states that "you must use our written move out form to ensure you provide the information needed". My plans have changed and on 5/29/12 I sent another e-mail to my property manager to let them know I no longer want to terminate my lease. The property manager replied by e-mail stating that they have already re-leased my apartment and the new tenant is scheduled to move in on June 17th and as such they cannot cancel my notice since the apartment has been leased by a new tenant.
Can they make me vacate the apartment?

Yes. They accepted your notice. On the other hand. I don't think they can force you out prior to 6/30. When was the lease set to expire?

If they can't have the apartment available on 6/17 for the new tenant, then that tenant may look elsewhere.