Financial adviser Chris Groves, 38, and son Connor, a primary five pupil at Udston Primary in Hamilton, crashed into the water at around 11.15am on Saturday.
They had been travelling on the southbound carriageway of the A725 from Whistleberry Toll towards East Kilbride when the Honda S2000 two-seater sports car left the road and plunged down an embankment at Bothwell Bridge.
Road conditions, including the low bright sun which, according to one witness made driving conditions "impossible", are expected to form part of the police investigation.
Emergency services rushed to the scene and police divers pulled the young boy and his father from the submerged vehicle, but both were declared dead at the scene.
A special service will be held today at Udston Primary to remember Connor, an only child.
The school's headteacher, Elaine Henry, said: "The school is shocked and saddened to learn of the tragic loss of Connor and his father. He was a bright, friendly, happy boy who was valued by all in the school community.
"He was a very actively involved pupil in all aspects of school life. The school was privileged to have had the opportunity to be part of Connor's life.
"He was indeed a credit to his family, and our thoughts and prayers are with his mum, family and friends."
Mourners, including Connor's classmates and staff at his school, packed out Hillhouse Parish Church in Hamilton yesterday as the community struggled to come to terms with the tragedy.
Reverend David Burt, who is also the chaplain at Udston primary, said: "We had virtually a whole turnout of staff, and not just teachers - dinner ladies, cleaners, everyone had come along. The mood was very sombre. A lot of people were in shock as the reality of what's happened sank in.
"I knew Connor to see and I knew a lot of his friends because they attended our Boys' Brigade and Sunday School. They were in tears. One of the parents said to me: 'How do I tell my nine-year-old that his best friend is dead?'.
"I was caught up myself in the traffic chaos on the bridge on Saturday because I was travelling back from a conference. I heard the news that it was Connor and his father on Saturday night when one of the parents phoned me."
He added: "We're a very close-knit parish and it's just a real tragedy. There's a lot of very upset people in the community."
Connor's mother Claire, who works at the Royal Bank of Scotland, had been married to Mr Grove for 10 years.
She had to formally identify the bodies of her husband and son yesterday and was being comforted at home later in the day.
A neighbour said: "For anyone to lose two members of their family in a terrible accident is so cruel and absolutely devastating. I don't know how she'll ever recover."
The accident scene, between the Raith Interchange and Whistleberry Toll, is not a known blackspot, although overnight frosts had created icy conditions.
Council worker John McQuaid was in the area with colleagues when the accident happened.
He said: "We were down here yesterday because the pathway was needing a repair, and we left to get more equipment from the depot.
"A lorry was parked on the bridge, and the driver was standing behind it, making sure everyone was going to the outside lane.
"When we got back from the depot the traffic was backed up."
Mr McQuaid said poor visibility created terrible driving conditions.
"The sun was very low, it was really bright, you couldn't see," he said."
Sergeant John Tait of Police Scotland, who is appealing for witnesses, said no other vehicles were involved.