Both players have signed two-year contracts, keeping them at Scotstoun until at least May 2017 and have committed their futures to the club just a week after Stuart Hogg and Lee Jones penned deals for the same length of time.
South African-born Strauss arrived in Glasgow in September 2012 and the 28-year-old has made 56 appearances for the GUINNESS PRO12 side. He has scored six tries and has captained the team.
The powerful Number 8 has featured regularly for the Warriors and will become eligible to play for Scotland in September 2015.
Speaking exclusively to glasgowwarriors.org, Josh Strauss said: "I've learnt a lot working with the players and coaches at Scotstoun and it was a good decision to move to Glasgow from South Africa.
"I've enjoyed the last three years at the club and I really like the group of players that are here. I've developed playing in the GUINNESS PRO12 and European Rugby Champions Cup and I'm happy to be staying.
"I'm ambitious and I want to win trophies and I believe I have the best chance of doing that at the Warriors."
Nakarawa arrived in Glasgow in the summer of 2013 and has gone on to make 30 appearances for the club.
The 6ft 6in second-row has 24 caps for Fiji and represented his country at the 2011 Rugby World Cup in New Zealand.
The 26-year-old has played in six HSBC Sevens World Series events.
Speaking exclusively to glasgowwarriors.org, Leone Nakarawa said: "Signing my first professional contract with Glasgow was a big move for me and I'm really enjoying playing for the club and I'm very happy living in the city.
"We have excellent players and coaches at Scotstoun and I believe I can continue to improve working with them.
"The supporters have been great with me since I joined and I'm delighted to be staying."
Glasgow Warriors head coach Gregor Townsend added: "Josh (Strauss) and Leone (Nakarawa) have made a big impact since they joined us and it's a big boost for everyone at the club that they're staying.
"We really appreciate the continued backing from Scottish Rugby to make these deals possible.
"Leone has worked really hard in training to adapt to the 15-a-side game, having predominately played sevens before arriving in Glasgow and he's now a regular in the Fiji national squad.
"He has a wide variety of skills, which gives us something different and he's versatile, being able to play in the second-row and back-row.
"Josh is part of our leadership group and has captained the side. When he first came over he settled in really well and has adapted quickly to our style of play.
"He will continue to have a big role to play at the club both on and off the pitch."
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