The Samoa forward will now remain with the Black and Whites until the end of 2023 campaign.
Sao, 29, has impressed since joining Hull from New Zealand Warriors last year and missed just two games this term.
“The new contract takes me into my third and fourth year at the club, and I couldn’t be happier to be extending my stay here," he said.
“Me and my family are settled here in Hull, and both them and myself being happy is really helping my performances on the field - I feel like I put my best foot forward last season, and have still got more to give for this club.
“As a squad, we weren’t where we wanted to be last season, but we understand as a group where we went wrong and have regrouped going into 2022.
“Everyone has had to face some harsh truths in recent weeks, but I firmly believe the changes being made are putting the building blocks in place for us to make improvements next season, and I’m really happy to continue to be a part of this group.”
Hull finished well off the pace in eighth spot but head coach Brett Hodgson said: "Ligi is one of the first names on the team sheet every week, and his consistency on the field over the last season shows you exactly why.
"He’s a really important asset to our pack, and the group as a whole.
“He brings energy and enthusiasm to the group, which to us in terms of culture is just as important as his ability with the ball in his hands.
“I’m certain there’s still more to come from him over the next two seasons having seen vast improvements in his game over the course of the last 18 months.
“Ligi is another important name tied down for 2022 amongst our forwards, alongside the likes of Chris Satae, Manu Ma’u, Andre Savelio, Joe Cator and new signing Joey Lovodua - and we’re hoping to add to that.”