The 27-year-old has been signed by head coach Alan Solomons to fight for the starting spot at No.10 with South African Carl Bezuidenhout and ex-Bath Rugby playmaker Tom Heathcote.
But despite admitting he is stepping into the unknown, Burleigh is confident he has the skills to make his move to Murrayfield and PRO12 rugby a success.
"If that's the way it is and I have to forge my way through, I like that," he told the Scotsman. "Competition brings the best out of everybody and I'd hate to be starting right from the outset and for it to be an armchair ride.
"I don't know a hell of a lot about European rugby - I haven't watched a lot, but Alan has informed me of what the competition is like.
"It's a different country; not many people know much about me. I've got to prove myself, but I'm looking forward to the challenge. Murrayfield has a lot of history - it's awesome to get the chance to play there."
And Burleigh admits he is looking forward to a fresh start at stand-off at this point in his career.
"A lot of those things come really naturally," he added. "I work on those skills all the time so I've got no issues adapting to being a starting ten.
"I played a lot of rugby as ten when I was younger. When I went through the grades in Canterbury I was a stand-off and also a fair bit at Bay of Plenty, my provincial side. Mostly I've played a lot of 12 and I've enjoyed that, but it's a new opportunity for me and something fresh.
"I've got to that stage where I've hit my end point in New Zealand and probably won't go any further. I want a fresh and new start somewhere else and I've definitely got that with Edinburgh."
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