Federici began his senior career at Wolverhampton Wanderers in 2003, but was only there briefly and soon switched to Torres. 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. A brief loan spell to Bristol City followed, before Federici made his Reading debut during the 2006–07 season. However, he was still unable to dislodge Marcus Hahnemann from the starting position, and remained second choice, even going on loan to Southend United in 2008. However, after this loan spell, an injury to Hahnemann gave Federici a prolonged run in the team, and he remained first choice for several seasons.
Federici started his career in 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 had trials at Sheffield Wednesday and Bolton Wanderers before a trial at Wolverhampton Wanderers led to him signing on a non-contract basis in February 2003 for the remainder of the season. After a season at Italian club Torres, he returned to England, undergoing a trial at Leeds United but failing to earn a deal.
He signed for Reading in January 2005 on non-contract terms, and was quickly loaned out to Maidenhead. He spent the second half of the 2005–06 season on loan at Carshalton Athletic. 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. He joined Bristol City on a loan deal on 29 August 2006, but was recalled on 27 October without making a first team appearance.
On 12 March 2007, Federici signed a two-year contract with Reading to keep him at the club until the end of the 2008–09 season. 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. For this performance, he was named the FA Cup "Player of the Round" for the 5th Round. However, in the replay on 27 February, Federici had a night to generally forget as Reading conceded three goals in the first six minutes.
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. Federici again featured as a half time substitute during a 3–3 draw at Blackburn Rovers after Marcus Hahnemann had injured his hand.
Federici joined League One side Southend United on a month's loan on 25 September 2008, making his debut in a 3–0 victory over Leyton Orient the following day. The loan was extended for a further month in October, the keeper eventually returning to Reading after making 10 appearances for Southend.
In December, shortly after returning from his loan spell, Federici signed a contract extension, keeping him with the club until the summer of 2011. 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. 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. 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.
For the new 2009–10 season Federici was given the Number 1 jersey after Marcus Hahnemann was released. He produced "two of the best saves" of his career in the Championship match against Swansea on 18 August 2009, saving a penalty and two close range shots in a match which Reading drew 0–0.
Federici was a key part of the Reading side that reached the FA Cup semi-finals in 2015, the first time Reading had reached the last four since 1927. 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. Reading boss Steve Clarke defended and praised Federici after the match, saying they would not have even reached that stage without his efforts.
On 27 May 2015, Federici signed for Bournemouth on a free transfer after his contract expired at Reading.
Bournemouth loaned Federici out to Nottingham Forest on 31 August 2017, in a deal that was scheduled to run until January 2018. His loan was rescinded on 11 September 2017, following an injury sustained on international duty that required surgery.
Federici played for the Australia U20 team in the 2005 FIFA World Youth Championship. He was invited to a training session with the senior Australia squad on 29 January 2007 prior to their friendly against Denmark in London, and then received his first full call up to the senior team for their match against Uruguay on 2 June 2007. Federici was also selected to play for Australia at the 2008 Beijing Olympic Games.
His first cap came just before the 2010 World Cup against New Zealand, and he was backup to Mark Schwarzer for Australia as an unused substitute for all three of their group games. He also had the option of playing for Marcello Lippi's Italy side due to his Italian ancestry. 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. Australia went on to win 3–0.As of 19 September 2016
As of 7 June 2016
Reading Player of the Season: 2014–15