Former Arsenal goalkeeper Taylor had been training with the Royals since being released by Manchester City at the end of last season.
Reading were keen to sign the 31-year-old as cover for Adam Federici but were waiting for fellow keeper Andersen to complete a move to crisis club Pompey.
The Dane did so on Saturday on a one-month loan deal, playing the full 90 minutes of Portsmouth's 1-1 npower League One draw with Bournemouth.
Reading director of football Nick Hammond told the club's official website, www.readingfc.co.uk: "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."