The 34-year-old arrived from Dinamo Zagreb last summer but did not make a single appearance during Chelsea's Premier League title-winning campaign having been stuck behind Thibaut Courtois and Asmir Begovic in the pecking order.
The 36-time Portugal international will remain at the club as cover next season, though, having put pen to paper on a new one-year deal.
"I am very happy to stay at Chelsea for another year. This season has been very successful for the club, and everybody has made me feel like a part of the family. I hope next season can be just as positive and we can win many more trophies," he told the club's official website.
Technical director Michael Emenalo added: "Since joining us last summer, Eduardo has been a model professional.
"He has used his wealth of experience at the top level to bring the very best from his fellow goalkeepers and has been a reliable, popular and respected member of the squad. We are delighted he has chosen to commit his future to Chelsea."
Eduardo has previously played for the likes of Braga and Genoa, and was part of Portugal's squad at the 2014 World Cup.