Police in Germany say a young Iraqi man has confessed to the murder of fashion designer Rudolph Moshammer.
Police say the suspect shaved his head after the crime was committed
The man, whom they named only as Herisch A, says he became embroiled in a dispute with Moshammer over payment for sex, police said.
Moshammer was found dead with a cable round his neck on Friday.
Moshammer, 64, built a reputation for the extravagant clothes he designed and wore, and was well known on Germany's celebrity circuit.
Herisch A, 25, was arrested on Saturday night, lead police investigator Harald Pickert told reporters on Sunday.
He said the man was identified because a DNA he had voluntarily donated to the national database for a previous investigation had matched traces of DNA found at Moshammer's Munich villa.
"After several hours of interrogations he made a confession," Mr Pickert was quoted as saying.
Herisch A says Moshammer approached him just before midnight on Thursday near Munich central station and they agreed Mr Moshammer would pay him 2,000 euros ($2,600) for sex.
But Moshammer reneged on the promise once the two returned to his home, and a fight broke out, the Iraqi said according to police.
Rudolph Moshammer was well known on Germany's celebrity circuit
"During this fight the 25-year-old suspect slung a cable around Moshammer's neck and strangled him," Mr Pickert said.
Police displayed pictures of the suspect, showing he had shaved his head after the killing.
Among Moshammer's clients were Austrian-born Arnold Schwarzenegger, now governor of California, tenor singer Jose Carreras and the Las Vegas-based magicians Siegfried and Roy.
Moshammer opened a boutique in Munich's most expensive street, Maximilianstrasse, in 1967, where he offered his fur, cashmere and silk garments.
In 2002, he sold a shirt thought to have been worn by Napoleon Bonaparte at the Battle of Waterloo at auction for more than 62,000 euros ($81,200), donating the proceeds to a Munich homeless charity.
He claimed to be 59 but was revealed to be 64 when he appeared in an Austrian court for a driving offence.
The designer's famed Yorkshire terrier Daisy, who accompanied him everywhere, is well and staying with Moshammer's chauffeur, police said.
"Everyone wants to know how the dog is," a police spokesman said.