The 26-year-old man had made it to shore with two friends who had been sharing the vessel after the incident on Loch Fyne in Argyll.
But within hours, while camping close to the sea loch, he took ill and was rushed to Mid Argyll Hospital in Lochgilphead, where he passed away.
Police have refused to comment on the cause of the man's death early on Sunday morning after he had fallen into the freezing waters between 4pm and 5pm the previous day.
They have also not released his identity at the request of his family.
A Strathclyde Police spokeswoman said: "The incident on Loch Fyne took place on Saturday, November 24, between 4pm and 5pm.
"Two of the three men involved were in a 15ft kayak on the loch which capsized.
"They both managed to make their own way back to shore where they then camped overnight.
"Around 6am on Sunday, November 25, the deceased's friend realised he was unwell and he contacted the Coastguard via 999.
"The lifeboat attended and took the men to Tarbert where they were transferred by ambulance to the Mid Argyll Hospital where, sadly, the 26-year-old man died a short time later."
The spokeswoman added that a report will be submitted to the procurator-fiscal and enquiries are continuing.
The incident was co-ordinated by Belfast Coastguard, which has taken over responsibility for duties in the area from Clyde Coastguard, which has effectively closed down.
Meanwhile, two male jet-skiers were rescued from the Tay estuary on Sunday afternoon after the jet-ski they were travelling on broke down.
A friend who was on another machine returned to shore and raised the alarm and a helicopter and lifeboat were deployed to rescue the men, who were taken to Ninewells Hospital.
A search for a person who was seen falling into the River Annan was also called off at around 2.30pm yesterday afternoon after drawing a blank.