Governor Rick Perry will sign an official declaration to that effect on August 20 at the Capitol in Austin, Texas.
The initial push to give the breed official recognition came from Logan Head, 10.
There will be quarter horses on the state grounds to mark the historic occasion.
The history of Texas is closely intertwined with the breed, beginning with Steel Dust, one of the forebears of the state's more than 470,000 quarter horses.
In the early days, the horses were used to help settle the wild and wooly territory. Then, they were used by ranchers to round up livestock and move them to market, as well as for a little match racing on the weekends.
The American Quarter Horse Association, the breed's registry, was started in 1940 at a meeting of ranchers and horsemen at the Fort Worth Fat Stock Show. It is headquartered in Amarillo in the Texas Panhandle.
Today, the breed is considered to embody the spirit of Texas and exemplify the versatility of his ancestors.
"This is a great way for the American quarter horse to be recognised," said American Quarter Horse Association executive vice-president Don Treadway.
"We need to give credit to the Texas Quarter Horse Association, Representative Larry Phillips and 10-year-old Logan Head, who got the ball rolling on this by writing to Representative Phillips with the idea of making the American Quarter Horse the state's official horse."
Logan is an American Quarter Horse Youth Association member from Bonham, Texas.
The signing of the declaration will follow the governor's signing of House Bill 1881, which establishes the Texas Equine Incentive Programme, creating a voluntary monetary incentive programme to keep quarter, paint and appaloosa horses breeding, showing or racing in Texas.