The 19-year-old, who can also operate as a forward, joins Javi Gracia's side after establishing himself as a first-team regular at Primeira Liga side Vitoria last season.
Horta made 28 appearances in the Portuguese top flight last season, scoring six goals for the club he joined from Benfica at the age of 16.
The teenager has made five appearances for his country at Under-21 level and scored three goals in the recent Toulon Tournament, including the only goal of the game against England.
Horta was also capped at Under-19 and Under-20 level for his country and will be hoping to force his way into the senior squad by making an impact in La Liga.
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