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Espanyol finished 14th in LaLiga in the 2021-2022 season, after gaining promotion back to the Spanish top flight as champion of the second tier.
However, it dismissed Vicente Moreno this month and have now moved for Martinez, which left Granada in May 2021 and has signed a two-year deal.
Martinez spent three seasons at Granada. He led the team back to LaLiga in 2019 before finishing seventh and reaching the semi-finals of the Copa del Rey in the following campaign.
A ninth-placed finish followed in the 2020-2021 season, along with a run to the quarter-finals of the Europa League, where it was beaten by Manchester United.
He opted against extending his stay at Granada, however, and the work he had done there was emphasised when the side went on to be relegated this season, finishing 18th.
In total, 41-year-old Martinez won 29 of his 76 LaLiga games in charge of Granada (38.16 per cent), losing 32 and drawing the other 15, with his side averaging 1.34 points per game.