Currently with the Fijian squad at the Rugby World Cup and preparing to face Wales at the Millennium Stadium on Thursday, Matavesi made his Ospreys debut on the opening weekend of last season, a 44-13 over Treviso at the Liberty Stadium.
In total he played 29 times in all competitions in his first year - a joint record for Ospreys appearances in one season.
Speaking after putting pen to paper, the former Racing Metro and Worcester man said that
"It was an easy decision" said Matavesi.
"I enjoyed my rugby last season, my family are happy and settled here, so committing my future to the Ospreys was the right thing to do. We love it here. We've settled in well, my daughter is in school now and she's happy, and that's important when making any decision like this.
"I feel that I've grown in this environment, which is geared to improving players, and I think that I can continue to develop here. While I'm away at the World Cup I'm still in contact with everybody at Llandarcy and watching how the boys are doing, and I know that we can't just walk straight back in and expect the jersey. That's how it should be, we have high standards and we know that anyone wearing an Ospreys shirt has to earn it."
Andrew Millward, Rugby General Manager at the Ospreys, said:
"Josh was someone we identified who could bring something different to our game, provide a point of difference, and he certainly made a huge impression last year.
"He's a good character, a real personality, and is someone with experience of various contrasting environments so he can be a positive influence on and off the field. What is key with Josh is that he is always striving to be better and, as good as he was last season we believe there is a lot more still to come from him.
"When he gets back from the World Cup we'll be expecting him to pick up where he left off last season and continue to be a key figure for us."