If there was no signed agreement that the tenant would leave a specific address on a specific date, then legally they do not have to move out. E-mail or text message notices or agreements are not valid.
If they have not paid rent that you or they assumed they would not have to pay if they were moving, then you can serve them a N4 – Notice to Terminate for Non-payment of Rent. The form will give the tenant 14 days (for a monthly tenant) to pay the rent or move out. If they fail to pay or move, you can apply to the Landlord and Tenant Board for an eviction hearing on/after the 15th day.
The correct form for an agreement to terminate (Form N11) is also on that page of the forms, should you need it in the future.
The forms and instructions are available at: http://www.sjto.gov.on.ca/ltb/forms/