Xylella fastidiosa is an economically important plant pathogenic bacterium of global importance associated, since 2013, with a devastating epidemic in olive trees in Italy. Since then, several outbreaks of this pathogen have been reported in other European member countries including Spain, France, and Portugal. In Spain, the three major subspecies (subsp. fastidiosa, multiplex, and pauca) of the bacterium have been detected in the Balearic Islands, but only subspecies multiplex in the mainland (Alicante). We present the first complete genome sequences of two Spanish strains: X. fastidiosa subsp. fastidiosa IVIA5235 from Mallorca and X. fastidiosa subsp. multiplex IVIA5901 from Alicante, using Oxford Nanopore and Illumina sequence reads, and two hybrid approaches for genome assembly. These completed genomes will provide a resource to better understand the biology of these X. fastidiosa strains.