James McConnell, 69, who is understood to be originally from Clydebank, landed in a reservoir.
The skydiving centre Thai Sky Adventures told the BBC it believed he may have had a heart attack or a stroke after leaving the plane on Thursday.
His son has posted a message on social media saying "Fly free my hero".
Mr McConnell was an experienced skydiver.
Thai authorities are investigating. The Foreign Office said it had been informed but did not want to confirm details of the man's identity.
News portal Khaosod quoted police spokesman Col Chonnapat Nawalak as saying: "We have to check whether he died from the jumping or from drowning."
In a post on Facebook, Mr McConnell's son Mark McConnell wrote: "It is with a heavy heart that I have to tell my Facebook friends and family that my dad Jim McConnell has sadly passed away.
"As soon as I can confirm what happened I will let you know but for now, the family and I would appreciate privacy at this difficult time! Blue skies to you all xxx.
"All of you who knew my dad will know that he went the way he wanted and no-one should feel sad, fly free my hero xx."
Harry Harrison, director of flight operations at Thai Sky Adventures, said the centre began its own investigation immediately after the incident on Thursday.
Eyewitnesses told the centre they saw the man rolling onto his back and spinning in mid-air shortly after he jumped.
His parachute was seen to be deployed, but he did not steer it as he drifted towards the ground. He missed the designated landing spot and landed in water.
Mr Harrison said the man was pulled out within five minutes by a rescue team, who tried to revive him.
It is the second death to have happened at Thai Sky Adventures, which opened in 2009. Last year a Russian instructor died during a jump, said Mr Harrison.
He said the causes for both deaths could not be attributed to the centre. "Our safety record is excellent," he said.
The centre was shut on Friday, but would resume operations on Saturday, he added.
A Scottish man has died while skydiving in the Thai resort town of Pattaya with a group of friends.