The details of the support by the Lawn Tennis Assocation (LTA), the Professional Golfers Association (PGA) and Tennis Scotland were released by the sporting duo as they continued to win over local opinion.
Hundreds have objected to the plans for the Park of Keir development between Bridge of Allan and Dunblane, with some claiming the plan is a “Trojan horse” to get the large housing scheme past planners.
Others campaigning against the centre say it would destroy the green belt and lead to a sprawling merger of the two towns.
More than 400 people have written to Stirling Council objecting to the plans and calling for them to be rejected - but now the three leading sporting organisations have leant their weight in favour of the centre, writing letters of support.
Davis Cup Captain, Leon Smith from the LTA said: “This tennis centre will create a special environment whereby both players and coaches can come together to learn from Judy and her coaching team and will greatly strengthen the likelihood of finding another Scottish Wimbledon champion in the future.”
Brian Mair from the PGA urged council planners: “This is our opportunity to demonstrate what Scotland has to offer and, most importantly, create a legacy that will benefit the sport and country in the years to come.”
And in a joint statement Tennis Scotland chairman Gordon Baker and president Ian Conway said: “In our experience, significant independent investments are few and far between and, given our ambitions to grow the game in Scotland on the back of a golden period for tennis, these proposals should be given serious consideration.”
The planned centre will include six indoor and six outdoor tennis courts, a six-hole golf course with practice range, mini golf, 3G multi-sport all weather pitch along with changing facilities, coaching suites, and a cafe restaurant.
The plans also includes 100 homes and a hotel on the 282 acre site.
Ann Shaw, of campaign group Residents Against Greenbelt Erosion (RAGE) said: “Her legacy looks like it will be that she destroyed the green belt between her home towns, taking away their identity and turning them into one big anonymous commuter town.”
Douglas Jackson of Bridge of Allan said plans for a science park in the same area were thrown out 25 years ago after the “true reason” for the development was revealed - developing 220 luxury homes.
He added: “Now we’re told, according to the developers’ website, that 100 luxury homes are an ‘essential part of the development’ of Mrs Murray’s tennis centre and golf course.
“She is asking the people of Bridge of Allan and Dunblane to finance her tennis centre by giving up an irreplaceable community resource.
“As one of them, I’d respectfully ask her to take her dream elsewhere.”
The developers said they had listened to locals’ feedback about the plans and said the housing is needed to ensure the development is built “debt-free”, reducing the cost of accessing the facilities.
They stressed that only 40 acres are being used for the sports facilities, hotel and housing, and said they are keen to talk to locals about making the rest of the green space into a “community park”, managed by locals.
The applicants maintain “an extensive permanent green belt” will be preserved between Dunblane and Bridge of Allan.
Murray, mother of tennis star Andy Murray and brother Jamie, said: “Park of Keir represents a once-in-a-lifetime chance for us to establish a sporting facility that is open to all near to my home towns of Bridge of Allan and Dunblane.
“I am passionate about this project and the opportunity it presents for us to create a lasting sporting legacy for the benefit of families across Scotland.”
Golfer Mongomerie, winner of over 40 international tournament titles and a former Ryder Cup captain, added: “This is a once in a lifetime opportunity to truly develop young sporting talent in Scotland, and I hope that the Park of Keir development will benefit aspiring young sports stars for many generations to come.”