The 31-year-old Papua New Guinea international, who has scored 158 tries since joining the Eagles six years ago including a club record 46 in 2013, joins team mates Duane Straugheir and Rob Worrincy in pledging his future to Sheffield who are to go full time in 2016.
Eagles director of rugby Mark Aston said: “We are highly delighted that Menzie is on board going forward.
“He has been a revelation since he joined the club many years ago and we are looking forward to plenty more years together as we enter the next phase in the history of Sheffield Eagles rugby league.
“He has been fantastic for us over a long period of time and we are excited about what he can bring in the future.”
Yere was ever-present in 2015 and a member of Sheffield’s grand final winning team in 2012 and 2013.