The 24-year-old was born in Mallorca and began his English career at Kidderminster Harriers in 2009.
He joined Charlton Athletic in 2011 before heading to the MLS with New York Red Bulls where he played 23 times.
Izquierdo then signed for NY Cosmos where he won the National Premier League MVP award and was part of their NASL Championship winning side in 2015.
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Barnet have signed Spanish winger Ruben Bover Izquierdo after he impressed on trial at the League Two club.