David Cox, 42, was driving his daughter Tess, 11, on the school run on Thursday (January 24) morning when he skidded off a narrow path and into the River Wye in Derbyshire.
Tess was able to escape the car and get safely to the river bank, but her father was trapped for around 40 minutes, and later died in hospital.
His wife, Ruth Cox, was driving their son Ioan, 9, to school at the same time and also spun off the bridle path, before plunging into the river.
But the 39-year-old mother and her son were both able to get out of the vehicle and swim to safety.
Mr Cox had been at the BBC since May 2010 and was a member of the Future Media team based at BBC North in Salford.
Tim Davie, who is acting BBC director general until Lord Tony Hall takes up the job in March, expressed the BBC's sadness at the death of Cox, who played a role in the corporation's coverage of the London 2012 Olympics.
"We are very sad to learn of David's tragic death. He was a popular member of the Future Media team in Salford and had been key to the success of the red button service during the Olympics in the summer," he said.
"Our thoughts are with his family, friends and colleagues here at the BBC at this difficult time."
Roux Joubert, the head of TV and mobile platforms at the BBC, added: "David was an important member of the team and played a central role in the department.
"He will be sorely missed by everyone here and our thoughts are with his family at this time."