Torrence helped USA win silver at the World Relay Championships in 2014 and won an individual silver of his own at the Pan American Games in 2015 before switching allegiances to Peru for the 2016 Rio Olympics.
Torrence competed in the men's 5,000m race in Rio, eventually finishing 13th as Great Britain's Mo Farah claimed gold.
"Detectives learned that there were no obvious signs of foul play," a police statement said.
The track world lost a great friend and athlete today. Rest in peace, David Torrence. pic.twitter.com/iaCtDuFErk— USATF (@usatf) August 29, 2017
Earlier this summer Torrence had set the Peruvian national record for the fastest mile and fastest 1,500m.