The 24-year-old Spain international joins the newly-promoted Cottagers on deadline day, putting pen to paper on a deal which will keep him at the club until the end of the 2018-19 campaign.
Rico, who is a Spain international, could make his debut for the club during their season opener against London rivals Crystal Palace on Saturday.
"I'm very happy, really pleased to have signed for the oldest club in the Premier League," Rico told the club's official website.
"I'm excited to start training, to meet all my teammates and, above all, to enjoy the season that starts this Saturday."
Owner Tony Khan added: "I'm excited to announce that Fulham Football Club has signed Sergio Rico on loan from Sevilla. Sergio is a world class goalkeeper, and thus, his services have been in great demand.
"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. Come on Fulham!"