McLachlan, who opened John Paul at the Marine at the MacDonald Marine Hotel & Spa in June 2011, said he was excited to be developing his first solo business.
He said: "I am delighted to have finally secured Bunney's as it is a site I have had my eye on for several years now.
"It is a great location in the heart of town and offers me the right facilities to develop a new venture. While this is my first business on my own, the experience and contacts I have established in the catering industry will help make this a successful first footing."
Bunney's, formerly known as the Fisherman's Kitchen, was owned and run by Rod and Lorna Bunney for 12 years before they decided to sell up in March of this year.
Daniel Arrandale, associate director at the Edinburgh office of Christie & Co, the agent in charge of securing the lease, said the 20-cover site had attracted 'significant interest' and the agency had received multiple offers.
"The level of interest was expected due to the prominent town centre location and the level of trade generated, particularly since the business was re-branded as Bunney’s in 2010," he said.
McLachlan, who worked with Raymond Blanc and Gordon Ramsay before opening John Paul at the Marine, said he planned to re-name the site JP’s Deli & Cafe, but was not planning any major changes.
"The business will remain much the same, but my plan is to develop a much wider range in our deli with a strong emphasis on locally sourced produce. The property is also licensed and the wines will of course be an area of the business I will be looking to enhance over time. I am also looking to develop the menu offering to capitalise on the 20 covers available to us," he said.