According to the BBC, it will be Scotland's first purpose-built centre for the two sports.
Located at Park of Keir, between Dunblane and Bridge of Allan, the facility will be part of the Stirling Sports Campus, which also includes the University of Stirling's sports facilities and the Forthbank sports complex.
The centre will have six indoor and six outdoor tennis courts, a nine-hole golf course with practice range, mini-golf and multi-sport artificial grass courts as well as changing facilities, coaching suites and a cafe.
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There are also plans for the wider development of the site and include a hotel, children's adventure park, woodland walks and mountain bike trails.
The new centre has been a long-term ambition for Murray's mother.
Speaking to the BBC, she said: "The centre will make both sports more accessible and affordable for families, but especially for youngsters.
"My aim is to create a real community hub that links with local clubs and schools to grow both tennis and golf in the Stirling area and can deliver a pathway to excellence for the most promising players and coaches."
Councillor John Hendry added: "These proposals fit well with our commitment to make sport a driver in improving health and wellbeing across society, encouraging all ages, but particularly the young, to become active in sport.
"Stirling is fast being recognised as Scotland's city of sport and this announcement strengthens our case for locating the National Performance Centre for Sport in the city".
A number of public exhibitions will be held during July and August to allow local residents to view the proposals.
Subject to further planning approval, work would begin on the facility during 2014.
(JP/CD)
