Eydmann, 41, is thought to have suffered a heart attack while swimming in Lake Como on Monday.
"Something happened when he dived into the water but as yet we don't know what," a spokesman for the British consulate in Milan said. Eydmann was taken to a nearby hospital in the town of Menaggio, and died on Wednesday.
Eydmann was managing British band Spitfire in 1991 when he met Suede singer Brett Anderson at a Christmas party. He took over the reins and was instrumental in Suede's first deal with Saul Galpern's indie Nude Records.
"I was very saddened to hear of his passing," said Galpern today. "Jon was a sweet guy, a very likeable person who played his part in the first exciting phase of Suede's career, including their Brits and Mercury nominations and the release of the first album which was the biggest-selling British debut of all time at that point."
Eydmann relinquished the role when new manager Charlie Charlton was brought in and went on to work with Luke Haines' The Auteurs and the Mega City 4. He also handled A&R responsibilities for Fire Records signings Spacemen 3, Libido and Novocaine and more recently his London-based Messy Lives Music was involved with Headswim, Kubrick, Sparks Lights and Flames and Hondo Maclean.
Suede biographer David Barnett has posted a memorial on his blog: http://thedavidx.livejournal.com/213035.html
"Jon was hilarious company," writes Barnett. "The last time I saw Jon was maybe 18 months ago when he invited me for a jam in the shed at the bottom of his garden in Finsbury Park - me on bass, him on drums, shouting out the chord changes as he bashed away. We were still in touch occasionally via Facebook and so on. He'd become a chef, was writing a cook book, doing a history degree and still dabbling in music. He was always enthusiastic and effusive about everything and I never heard him say a bad word about anyone. It's a terrible, terrible tragedy."