Secured his first Open Championship start on July 4 at the Dubai Duty Free Irish Open.
Three places at The Open were available and Veerman, who shared the lead with four holes remaining, ultimately took the final spot behind Lucas Herbert and Rikard Karlberg.
The American, who has a Dutch father and mother of Indonesian heritage, went to Mount Juliet 350th on the world rankings after five top-10 finishes on the European Tour last year.
The best of those was a tie for fourth at the Aphrodite Hills Cyprus Showdown won by Robert MacIntyre in November.
Five years ago he won a play-off for the Taifong Open on the Asian Development Tour and he has since had three runner-up finishes on the main Asian circuit.
Veerman had an eventful end to this May, coming through a qualifying event for the U.S. Open in Texas and then having flight delays that led to him playing the first round of the European Tour event in Denmark with borrowed clubs and very little sleep.
He competed at Torrey Pines in California three weeks later, but missed the halfway cut.