After a reasonably successful season for the Italian side, he joined Reading in 2005, and, following loan spells at Maidenhead United, Northwood and Carshalton Athletic, turned fully professional in 2006.

Federici started his career at Huskisson Football Club, south-east of Nowra, and was part of the Australian Institute for Sport before moving to England at the age of 17.

Federici signed his first professional contract for Reading in the summer of 2006, and in a subsequent pre-season friendly match on 15 July, scored the only goal of the game against Bromley, having been played as a makeshift striker.

[6] On 17 February 2007 a "second string" Reading side unexpectedly drew 1–1 with Manchester United during an FA Cup 5th Round tie at Old Trafford, with the young Aussie keeper making some fine saves in a memorable game for the club.

Federici made his league debut in Reading's 1–0 defeat away to Tottenham Hotspur on 1 April 2007, where he came on as a substitute at half time due to a hip injury to first choice goalkeeper Marcus Hahnemann.

[14] During December, Federici also started a run of first team appearances for Reading, due to a calf injury sustained by longtime first-choice stopper Marcus Hahnemann against Blackpool, keeping the American goalkeeper out for several weeks.

[15] After coming on as a late substitute in that game, Federici went on to make his full league debut between the posts against Norwich City, drawing praise from manager Steve Coppell for his performance.

[16] On 26 December 2008, Federici scored a 96th-minute goal from a rebound after Michael Duberry had a header cleared off the line from a Stephen Hunt corner, to give Reading a late equaliser in their 1–1 draw against Cardiff City.

In the semi-final, after making important saves throughout the match, Federici was at fault for Arsenal's extra-time winner from Alexis Sánchez as he allowed the shot to slip out of his hands and between his legs.

[35] On 11 October 2011, Federici started in a World Cup Qualifier match against Oman where he made a great save from a free kick from Ahmed Mubarak.