McNair, who founded the farm in 1994 with his wife Janice, said in a statement the time demands of running the Texans led to his decision to sell the 2,000-acre farm in central Kentucky and the training center in Aiken, S.C.
Approximately 80 horses in training and an additional 170 or so broodmares, yearlings, and weanlings were included in the deal.
"Janice and I have loved every minute of owning Stonerside but I have a duty to the Houston Texans now and it has become increasingly difficult to focus on both ventures," McNair said.
Darley spokesman John Ferguson said there are no plans to change the operation at Stonerside and that it will be "business as usual" for the farm going forward.
"Sheikh Mohammed is delighted to have been given this opportunity," Ferguson said. "Stonerside have bred some great horses in the past and we are confident it will continue to do so."
The McNairs will keep one horse in training, 3-year-old graded stakes winner Cowboy Cal – ninth in this year's Kentucky Derby – and retain their homebred stallions Congaree, Bob and John, and Stonesider, as well as their other stallion interests.
The acquisition is the latest in a series of aggressive moves by the sheik to gain larger control of the horse breeding market. Dubai's connection to the thoroughbred industry increased in April when a Dubai company whose leader is a close associate of the sheik announced it was purchasing Lexington-based Fasig-Tipton – North America's oldest thoroughbred auction company.