The 27-year-old rose through the ranks at Bay of Plenty before becoming a regular in the southern hemisphere's top-flight Super Rugby competition. He made his breakthrough with Chiefs in 2010 and continued his rise with a 2012 move to the Dunedin-based Highlanders, where he has been a consistent performer, making 32 Super Rugby appearances to date.
Alan Solomons, Edinburgh's head coach, said: "He comes very highly rated and regarded. He is a strong, physical and intelligent player and that will be a big help to us. We've signed him primarily as a stand-off but he is also comfortable at 12 and 13, which is important, in terms of intensifying squad competition and facilitating future rotation."
Burleigh will arrive at the end of the 2014 Super Rugby season, the date dependent on Highlanders' participation in the knockout rounds of the tournament. They are poised to earn a place in the play-offs. He said: "Alan Solomons talked me through his vision and the squad for next season. It sounds like he's building a good future, moving to competing further up the table and getting back into the European Rugby Champions Cup."