The 34-year-old is renowned as a strong scrummager and has vast experience playing in New Zealand, France and England, with Leicester boss Richard Cockerill - himself a former front rower - describing Stankovich as 'a natural prop forward with huge knowledge and experience'.
Stankovich has spent the past seven seasons with the Tigers since joining from French outfit Albi, winning English Premiership crowns in 2009, 2010 and 2013, and Jones believes he will have a big impact at Rodney Parade.
"We are delighted to have made such an experienced addition in Boris, who has been a member of a very impressive Leicester scrum," said Jones.
"He is going to bring vast knowledge and experience to the front row department. Currently we are young and inexperienced. Boris' guidance and leadership within this department will be crucial in helping our growth. We are convinced we have signed the right man."
New Zealand-born Stankovich, who can play both sides of the scrum and has made 113 appearances for Leicester since 2007, has been impressed with the progress the Dragons have made under Jones and namesake Kingsley so far this season.
The former Bath and London Irish player admits that the ambition of the region played a big part in his decision to move to Newport and he intends to do all he can to ensure that continues across the next two years.
"The opportunity to play in Wales at Newport Gwent Dragons under both Lyn Jones & Kingsley Jones is certainly one I am very much looking forward to," said Stankovich, who began his career as a hooker.
"The Dragons are an ambitious club and the region as a whole has been an integral part of Welsh Rugby over the years. That's something I will be proud of representing over the next two seasons."