The 29-year-old was named Golden Glove winner at the 2019 Women’s World Cup, and picked up a runners-up medal after the 2-0 final defeat by the USA.
She played 12 games for the Gunners last season, and leaves the Women’s Super League side after five seasons.
“Atleti has proven its worth in women’s football,” Van Veenendaal said.
“The club offers me the best conditions to continue developing as a goalkeeper. I can’t wait to start.”
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BBC Sport has launched #ChangeTheGame this summer to showcase female athletes in a way they never have been before. Through more live women’s sport available to watch across the BBC this summer, complemented by our journalism, we are aiming to turn up the volume on women’s sport and alter perceptions. Find out more here.