Ticket prices start from £11.70 for an adult single with services running every two hours, taking about 90 minutes.
Under 22s, over 60s and people with a disability can travel for free with a valid concession pass.
Sarah Elliott, commercial director for Stagecoach East Scotland, said: “There’s an exciting summer golf season ahead, and we’re ensuring visitors can enjoy convenient, hassle-free travel direct to the home of the sport from Edinburgh Airport.”
St Andrews is recognised as the oldest golf course in the world, where the game has been played for over 600 years.
The Old Course is a pilgrimage site for golfers worldwide.