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The hotel currently has 14 bedroom suites, a chapel, reception hall, two drawing rooms, conservatory, dining room, library and meeting rooms.
It is set in 50 acres of woodlands and garden with a trout loch.
Murray plans to transform the Victorian mansion, where brother Jamie married Colombian bride Alejandra Gutierrez in 2010, into a five-star venue and attract more visitors to the area.
The tennis star said he was "pleased to be able to give something back" to his home town.
The refurbished hotel is scheduled to reopen next spring ahead of the 2014 Ryder Cup, which is being staged a short drive away at Gleneagles.
Murray said in a statement: "I am pleased to have acquired Cromlix House and look forward to securing its future as 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."
Its previous owners of more than 30 years, the Eden family, said they were happy the venue was staying in local hands.
The hotel will boast a Chez Roux restaurant. Renowned chef Albert Roux, owner of Le Gavroche in London, is one of a group of industry experts consulted by Inverlochy Castle Management International (ICMI) which will manage Cromlix House on behalf of Murray.
ICMI managing director Norbert Lieder said: "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."
