The 23-year-old, who has played just 18 minutes this season due to multiple calf injuries, confirmed his new deal on Thursday.
A seven-Test Wallaby, his commitment will keep him on the books for next year's showpiece event in Australia.
Kiss, Lynagh's coach at the Reds since 2023, will take over as Wallabies coach from Joe Schmidt in August.
"Les has been very good over the past few years," Lynagh, who has added 6kg of muscle in the gym while rehabilitating this year, said.
"I like the way he thinks about rugby and the game plans he's installed where there is freedom to express yourself.
"I've said it before. It's a strong environment to improve in as a No.10."
Lynagh's selection at No.10 to face the British & Irish Lions last year made history, given his World Cup-winning father Michael did the same in 1989.
In a crowded race to wear the No.10 at next year's World Cup, he'll now get a chance to tick another box after his dad starred with the Wallabies in their 1991 triumph.
"At times, I still pinch myself that it happened," Lynagh said of his three Tests against the Lions.
"I was a kid in London watching the Wallabies at the 2015 World Cup and that inspired me to become a rugby player.
"To wear the gold jersey is something very special.
"The goal now is to get fit and healthy and get some good footy under my belt so I can contend again this year and in what will be a massive year in 2027.
"Nothing is given so I know I've got hard work ahead."
Kiss won't have Lynagh's services for a clutch clash with Moana Pasifika in New Zealand on Saturday as the sixth-placed Reds aim to secure a finals berth.
"Tom is a prodigious talent albeit this has been a difficult season for him so far," the coach said.
"His growth has been fantastic in recent seasons.
"Playing against the Lions last year was just a glimpse of what is possible in his future."
