The Australian recovered from a dreadful start to complete the comeback from 5-1 down, becoming the only the eighth player to win the World, UK and Masters titles.
Selby, who on Saturday made snooker’s 100th official maximum as he won his semi-final against Ricky Walden 9-5, opened the final with a 130 and quickly built a big lead.
But world number one Robertson crucially took the last two frames of the afternoon session and back-to-back centuries brought him level at 6-6.
He won the next two frames as well and pinched the 16th on the black when Selby left a simple pot for the frame over the corner pocket to move within a frame of victory, which he completed with a 57 break after Selby had built up a lead.
“When I beat John Higgins earlier this year in the Wuxi Classic, I said that was the best I’d ever played in a final but the second session tonight was definitely the best I’ve played in a final,” he said.
“To become the first overseas player to win all three, Ding Junhui and I basically turned pro at the same time 10 years ago and to get it ahead of him is a fantastic achievement.”
Selby on top
Both players were straight into their stride with fine long reds but it was Selby who was able to go on and take the opening frame with an impressive clearance.
A 63 after a long safety battle drew Robertson level but Selby made 49 in the next and eventually took the frame.
And breaks of 39 and 35 were enough for a 3-1 lead, the latter after a good safety forced Robertson into an attention-all-pockets thrash.
He won the first two back as well, Robertson missing a bad black in the second and also failing to take half-chances on the yellow and green.
The Australian finally narrowed the deficit in frame seven, though he had to work hard for it after a 54 break was ended when he fouled a pink in potting a red.
And he took momentum from that to win the final frame of the session. On 46, he had to ask referee Brendan Moore to reposition the black as it was rocking off its spot to block his next red, but with the problem resolved he went on to make 123.