Taylor has been a free agent since leaving Manchester City at the end of last season and after a successful trial period with the club, the Royals offered the former England youth international a one-year contract.
And Taylor's arrival at the club has seen young Danish goalkeeper Mikkel Anderson leave the club, joining Portsmouth on a one-month loan deal.
Reading's director of football Nick Hammond told the club's official website: "I'm delighted to have signed Stuart, he is a very experienced goalkeeper at the top level and having him here allows us to loan Mikkel Andersen out and get him some games.
"Mikkel was very patient last year, he is an outstanding goalkeeper and did a great service to the team last season supporting Adam Federici so has fully earned the opportunity to go and play."
Reading got their Premier League campaign underway with a 1-1 draw against Stoke on the opening day of the season, in which first-choice keeper Adam Federici made a howler to allow Michael Kightly's shot to slip past him at the front post.
The Royals' next game is a tough test against Chelsea at Stamford Bridge on August 20, before their meeting with Sunderland on Saturday at the Stadium of Light.