The world number 69 last contested a final in 2012 when she lost to fellow American Serena Williams at Stanford, and Zheng Jie will be her opponent in the Netherlands.
Vandeweghe only needed 70 minutes at the WTA International grass-court event as she impressively defeated the 2005 champion 6-4 6-2.
The first set swung on a run of three consecutive breaks from the third game onwards, with Vandeweghe emerging from that spell 3-2 up with the serve.
She did not look back from there and the 22-year-old seized her third set-point opportunity before breaking Koukalova in the Czech's first two service games of the second.
It took just one match-point opening for Vandeweghe to seal the triumph and set up a meeting with Zheng.
The Chinese will be looking for her fifth WTA title in Saturday's showdown after she swept aside the challenge of Magdalena Rybarikova 6-1 6-3.
Having won the opening five games of the match, Zheng allowed her opponent to get off the mark after spurning a set point on Rybarikova's serve.
She did not let that worry her, though, and moved into a 1-0 lead in the next game, only conceding 14 points in the set.
The second set saw the pair lose serve six times between them, but a crucial break from Zheng in the final game ensured her progress in 58 minutes.