Yes, you must:
From 28 March 2007, Royal Decree 240/07 requires that all EU citizens planning to reside in Spain for more than 3 months should register in person at the Oficina de Extranjeros in their province of residence or at designated Police stations. You will be issued an A4 printed Residence Certificate stating your name, address, nationality, NIE number (Número de Identificación Extranjeros) and date of registration.
Under the new rules, EU citizens applying for residency in Spain may be required to produce evidence of sufficient financial means to support themselves (and dependants). Applicants may also be asked for proof of private or public healthcare insurance.
https://www.gov.uk/residency-requirements-in-spain