Rico was an integral part of the Sevilla squad for four seasons and won the Europa League twice before losing his position as first choice keeper last season.
"Sergio joins a very talented cast of goalkeepers under contract at FFC, and he answers our mandate of making our squad the strongest and deepest it can be as we face top Premier League opposition," Fulham's director of football operations Tony Khan said in a statement.
Rico could feature in Slavisa Jokanovic's squad when they host Crystal Palace in their opening league match on Saturday.
Fulham also confirmed the signing of left-back Joe Bryan from Bristol City on a four-year contract, with an option to extend by a further year.
The club announced the signing of 24-year-old forward Luciano Vietto from Spain's Atletico Madrid on a season-long loan after the transfer window closed.
(Reporting by Hardik Vyas in Bengaluru; Editing by William Maclean and Peter Graff)
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