A sublet, or sublease agreement, adds someone new to an existing lease. The sublease legal document requires the full legal names, dates, and original signatures of both the sublessor (original tenant) and sublessee (new tenant).A sublease agreement is a legal document that permits a tenant to rent out their property to another person, known as a subtenant. A California sublease agreement is a written arrangement that involves a residential tenant leasing their rental property to a subtenant. You can't sublet a place you're no longer leasing. It is intended for use when a tenant wishes to sublease or assign his or her leased property to a third party, referred to as the "subtenant. About this Form: This form is known as a sublease or sublet agreement -- or as an assignment of lease. A tenant can legally sublet the rental property if stated or not mentioned in the lease. I signed a sublease agreement that the sublesor typed up. It only includes our names, the rent payment, the person I.