The artist, who has lived in Britain for 12 years, beat video artist Phil Collins, poster artist Mark Titchner and sculptor Rebecca Warren.
The judges said the 38-year-old had produced "compelling images that reveal their complexity slowly over time".
Artist Yoko Ono presented the £25,000 prize at London's Tate Britain.
Abts, whose paintings always measure 48 x 38 cm (19 x 15 in), said it was "a real honour" to receive the prize.
It looks like a screwed up paper bag that someone's flattened out again and stuck to a wall.
Very odd these Turner Prize Judges. I dread to think what the runner's up looked like if that won!
Brian Sewell once commented on a Damian Hirst and a Renoir. He pointed to the Hirst and said, 'I could do that' and then turning to the Renoir, said 'but I couldn't do that'. I think that says it all.
It does really.
Though I'm not sure why anyone would want to do anything like Damian Hirst. His stuff is very disturbing I think. Though I guess it's supposed to be?
It's worth noting that the Turner prize is for contemporary art so it's supposed to be different, challenging, promote debate and push the boundaries.
