The 34-year-old Stankovich has made 113 appearances for Tigers since arriving from French side Albi in the summer of 2007. He made his debut for the club in a victory at Bristol in the opening game of the 2007/08 season and has become a key member of the first-team squad, sharing in Premiership title wins in 2009, 2010 and 2013.
Tigers director of rugby Richard Cockerill said: “Boris is a natural prop forward with huge knowledge and experience in his position and he has been a very important part of the squad in the last seven seasons.
“He has been a great for us both in the first-team and in working with younger players in the squad and he will continue to do that for the rest of the time he is here.
“He will leave in the summer with our very best wishes for the future. We have a good group of props at the club and we’re also looking at our front-row options for next season.”
The Dragons have announced that Stankovich has agreed a two-year contract at Rodney Parade.