Yes, in Washington, D.C. a contract to lease is legally binding once both landlord and tenant agree to the essential terms (rent, property, and lease duration) and sign the agreement. Leases longer than one year must be in writing to be enforceable, and after signing, both parties must follow the lease unless there is a valid termination clause or other legal reason to end it early.
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The information for this answer was found on our Washington D.C. Residential Lease Agreement answers.