The Victorian hotel, situated close to Murray's home town of Dunblane and where his older brother Jamie wed Alejandra Gutierrez in 2010, is currently closed for extensive refurbishment and will re-open next spring.
Confirming his purchase, Murray said he planned to build 'a successful business'.
“By re-establishing Cromlix as a leading luxury hotel at the heart of the Dunblane community we will be able to attract new visitors to the area, create a number of new jobs and focus on supporting other local businesses. I’m pleased to be able to give something back to the community I grew up in," he said.
Inverlochy Castle Management International (ICMI), who already manage eight other independent properties around Scotland, including Inverlochy Castle and The Atholl in Edinburgh, will manage the hotel on behalf of its new owner with its re-opening expected to create 40 new jobs.
Chef Albert Roux's involvement with ICMI will also continue with Cromlix House where he will open a Chez Roux restaurant offering fine dining using locally sourced produce.
ICMI managing director Norbert Lieder said: "We are delighted to be working with Andy in this very exciting project to redevelop and run Cromlix House.
“Our team of experts has experience in every aspect of the hospitality industry and specialise in working with independent properties and transforming them into luxurious destinations.
“I am confident that, with Andy, we can create a very special hotel in his home community. While we aim to create a destination that attracts visitors from around the world we are also determined to ensure it remains a venue of choice for local people.”
Cromlix House was run by the Eden family for 30 years before it was bought by Murray. Set within 50 acres of secluded woodlands and garden, it boasts 14 bedrooms, a chapel, reception hall, two drawing rooms, conservatory, dining room, library and meeting rooms.