World champion Littler was in devastating form as he hit seven 180s on his way to an 8-4 victory and the £35,000 first prize.
Van Veen, who also lost to Littler in the final of the World Championship, hit his first ever televised nine-darter but it was in vain as the Briton averaged just over 108 to overcome the Dutchman.
Victory sees Littler become the inaugural champion at the tournament which is the first European Tour event to be held in Poland.
"It's been a very good weekend for myself," said Littler, who won his fifth European Tour title.
"I felt really good throughout the tournament. In the first three weeks of the Premier League I've not felt the best, so I definitely needed this one.
"I wanted to come here and win the title and that's what I've done. Most importantly it was about playing well, getting that average up and hitting my doubles."
Littler beat Ross Smith, Josh Rock and Chris Dobey on Sunday to make the final, while Van Veen got past Nathan Aspinall, Wessel Nijman and world number two Luke Humphries.
Van Veen took control of the match to go 3-2 up in the fifth leg when two 180s were followed up by a 141 finish in a perfect nine-dart leg.
The moment sparked Littler into life, however, who won the next four legs to take a 6-3 lead.
Van Veen showed some resistance to claw a leg back, but Littler regained his composure to win the next two legs in just 28 darts to seal an 8-4 victory.
The European Tour will continue with the European Darts Trophy on 13 March as Aspinall bids to retain his crown in Gottingen.
Final
Semi-finals
Quarter-Finals
Round Three
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