No financial details were given.
The Spanish-born midfielder represented England at under-17 level and was second tier Charlton's player of the year last season despite not making his debut until January.
"It's massive to come to a Premier League club," Poyet told the club's website. "I wanted a new challenge and soon as I heard there was a chance of stepping up I had to take it."
(Reporting By Tom Hayward, editing by Alan Baldwin)
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