The 30-year-old made 245 appearances for the Royals and was part of Australia's 2010 World Cup squad.
"It was difficult to leave Reading - I had been there an extremely long time," he told Bournemouth's website.
Federici was a free agent after the expiry of his contract, and now joins Bournemouth ahead of their first Premier League season.
"I feel like I'm joining something special and I'm looking forward to working with the manager and the boys. I can't wait to get started," he added.
"I had a lot of success at Reading and the fans were great for me, but I thought it was time I moved on."
Federici is the second goalkeeper signed by the Cherries this week after Artur Boruc, joined from Southampton on a one-year deal.
He played 49 games for Reading this season, including the FA Cup semi-final against Arsenal, but let Alexis Sanchez's shot slip through his hands as they were defeated at Wembley.
But a career highlight was his injury-time goal for Reading in a 1-1 draw with Cardiff at the Madejski Stadium in 2008.

The firm said that it was working to boost capacity at telephone exchanges in the worst hit areas.
The news coincided with the launch of Sky Go Extra - a service allowing users to download movies and TV shows so they can be watched offline.
One expert said the product might add to the strain.
Sky Go Extra still works at slow internet speeds - however, Sky's other streaming services rely on the user having a 2 megabit per second connection. Some subscribers have complained their download speeds have fallen below this level at peak times.
A Sky spokeswoman apologised for the problems.
"Following a combination of an underlying increase in network traffic as well as a high rate of new customer additions, we are aware of capacity issues in a small number of exchanges," she said.
"We are working on adding new capacity to those exchanges as quickly as we can. We apologise to all customers who have been impacted by this issue."
She confirmed a report by The Register that users in Doncaster, North Wales and Bristol were among those affected, but declined to be more specific or name other locations.
However, the firm has provided an online postcode checking facility for its subscribers to check if their local exchange has been flagged as having an issue.
Sky also indicated that less than 5% of its broadband customer base used the affected exchanges.
Andrew Ferguson, editor of the Thinkbroadband news site noted that Sky had recently run a major promotion highlighting the fact it did not place "fair use" caps on the amount of data its customers use.
As a result, he said, the firm had probably attracted subscribers who downloaded significantly more than the average 23 gigabytes per month consumed by the average UK broadband user.
"Sky had this problem last year in some of its exchanges, and it's definitely not the only service provider to have experienced this problem," he told the BBC.
"It's very much related to the firms' promotional activities. Sky has also been pushing its fibre products recently - they offer higher speeds and people who sign up generally use more data afterwards."

Tanveer Iqbal's body was found in his Renault Clio in Portland Road, Edgbaston, on Monday afternoon.
The 33-year-old had not been seen since closing his Hi-Tech Music shop in Shireland Road, Smethwick, on Sunday evening and had been reported missing.
Police said his death is currently being treated as suspicious and a post-mortem examination will be carried out.
Mr Iqbal was reported missing at midday on Monday.
More on this story and others from Birmingham and Black Country
Portland Road was cordoned off between City Road and the Ridgeway and the car has been taken away for investigation.
Det Insp Paul Joyce said police are working "around the clock" to try to piece together Mr Iqbal's last movements.
"Portland Road is likely to remain closed until later today while my team continues to carry out an important forensic examination at the scene," he said.
"I am particularly keen to speak to any witnesses who may have seen Mr Iqbal between closing his shop in Smethwick on Sunday night and the time he was discovered at lunchtime on Monday."
AFC Bournemouth have signed Australia international goalkeeper Adam Federici from Reading on a three-year deal.
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Sky has acknowledged that some of its customers are experiencing slow internet speeds as a consequence of it signing up new subscribers.
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The body of a missing music shop owner has been found in the boot of his car parked in Birmingham.