The 34-year-old will be remembered as one of KR's best overseas signings of the summer era after showing remarkable consistency across his five seasons with the club.
Linnett scored 40 tries in 110 appearances to help the Robins reach three semi-finals in addition to this year's Challenge Cup showpiece at Wembley.
The Australian, who represented Scotland at international level, earned a place in the 2021 Dream Team at the peak of his powers in Super League.
Linnett won the Grand Final with North Queensland Cowboys during his time in the NRL and was a runner-up twice, once with first club Sydney Roosters.
The converted back-rower was under contract for 2024 but has decided to bring forward his retirement.
"After thinking about my future thoroughly, I’ve made the decision to finish my professional rugby league career and head home to Australia," said Linnett, who made 306 appearances at the top level.
"I’ve given my all for the badge, supporters and my team-mates for the past five years and feel like the time is right for me to finish up and chase a new adventure.
"I’m very proud of how far Hull KR have progressed since I first arrived and it’s exciting to see where the club is going.
"I have so many great memories that will last a lifetime and I’m forever grateful for the opportunity that Hull KR have given me and my family.
“The club, the fans and the city will always hold a special place in my heart."
Linnett's retirement frees up an overseas quota spot, which is expected to be filled by Tanginoa.
Willie Peters will have a new-look left edge in 2024 after Shaun Kenny-Dowall also called time on his career.
"On behalf of everyone at Hull KR, we’d like to congratulate Kane on an outstanding 14-year career," said the Rovers boss.
"Kane is a leader of men who leads through his actions both on and off the field. He’s a great character with a strong work ethic who I’m sure will be successful post-rugby in anything he sets out to achieve.
"Kane has been an important part of Hull KR and will leave a lasting legacy at this club. He has achieved the highest of accolades in the game and we wish Kane, Erin and their children all the best for the future."