The businessman was piped to the first hole of the Aberdeenshire course and teed off with former Ryder Cup captain Colin Montgomerie.
Montgomerie said it was an "honour" to play the first round on the "marvel" of a course.
Sandy Jones, chief executive of the PGA, and George O'Grady, chief executive of the European Tour, said they would work to bring major golf events to the course.
Mr Trump cut a ribbon on the first tee and said: "When I bought this land almost seven years ago we said we wanted to make the best course in the world and some people are already saying we have done that.
"I think this is great for golf, and what's great for golf is great for Scotland because it's the home of the game."
The building of Trump International Golf Links in Aberdeenshire has been controversial, with environmental campaigners opposing the construction of the course on protected sand dunes and Mr Trump himself complaining about a potential offshore windfarm being built near the site.
The course will open to the public on Sunday July 15, with a series of private events being held this week.
Millions of pounds have been spent on the course and the clubhouse, but further plans for a hotel and homes in the area have been put on hold until a final decision is made on the offshore windfarm proposal.
Trump International said 160 jobs have been created so far with positions in management, catering and course maintenance.
Work on the course began in July 2010 after the tycoon won planning permission to start work on the construction four years after plans were first put forward.