The 27-year-old Australia international joined the club in 2004 and his previous deal had less than 12 months to run.
Federici said: "It's absolutely great to have signed this new contract.
"I've been here a long time, I've put in a lot of blood, sweat and tears so it wouldn't have been right to do anything other than sign again.
"The club has got great backing, there's a really good feel around the place, the club is only going in one direction and that's upwards."
Royals chairman Sir
"He is part of our backbone and was so vital in getting us promoted again.
"He has a tremendous pedigree and I'm over the moon he has signed for us once more because he is without doubt one of the best goalkeepers in the country."
The club's director of football
"Adam was the best goalkeeper in the Championship last year and I think he will prove to be one of the best in the Premier League as well.
"He is a magnificent example to young players of what can be achieved when hard work and dedication are allied with talent. We are all delighted that he has signed."
"I have known him for a number of years now, it seems like time has flown and he has constantly been developing into a top class goalkeeper.
"He is a lesson to young professionals about what is required to get to the top of your game.
"His workrate, diligence and desire are second to none and we're delighted he's chosen to commit to us again."