Jimi Heselden, 62, was found in the River Wharfe at Boston Spa, near Wetherby, yesterday morning and died at the scene.
It appeared Mr Heselden, whose company builds and markets the Segway upright scooter, accidentally drove over a cliff into the river. It is understood one of the machines was found nearby.
Members of his family, many of whom paid an emotional visit to the scene of the accident this afternoon, described their grief at Mr Heselden's death.
A family spokesman said: "Our family has been left devastated by the sudden and tragic loss of a much-loved father and husband.
"While we have been touched by the many kind tributes to his life and career, some of the speculation as to cause of his death has been deeply upsetting. There is absolutely nothing to suggest it was anything other than a tragic accident.
"The exact circumstances of the accident are still being clarified and will, of course, be the subject of an inquest.
"We would once again like to thank Jimi's many friends and colleagues for their help and condolences at this very distressing time for the family."
There was little evidence of the accident today in the remote wooded area next to the River Wharfe, which is not far from the tycoon's estate in the countryside to the north east of Leeds.
One area of the woodland path at the top of cliff faces on the river's banks - which is accessible from a public bridleway - is particularly uneven with a sheer drop of around 30ft down to the river.
The heavily wooded area, which is popular with walkers, has areas of relative flat before being broken by various tree roots and branches.
Mr Heselden made his fortune when his Leeds-based firm Hesco Bastion developed the "blast wall" basket, which protect soldiers in Afghanistan and Iraq, as a replacement for traditional sandbags.
Last year he led a British team which bought the US-based Segway firm, which makes and distributes the distinctive two-wheeled, self-balancing scooters.
Mr Heselden was as well-known for his charity giving as he was for his massive fortune and tributes poured in for him from various sectors.
Tom Riordan, the chief executive of Leeds City Council, said: "We are all devastated and saddened to hear of the tragic death of Jimi Heselden OBE.
"Jimi was an amazing man who, apart from being a wonderful success story for Leeds due to his business acumen, was also remarkably selfless and generous, giving millions to local charities to help people in his home city."
Staff and trustees of the Leeds Community Foundation said they were deeply saddened by today's news.
They said the foundation has been working closely with Mr Heselden since 2008 when he made a £10 million donation to set up the Hesco Bastion Fund.
He went on to donate a further £13 million to the fund, which supports local projects in east and south Leeds, major health initiatives and Army-linked projects.
Chief executive Sally-Anne Greenfield said: "It was a real privilege to have got to know Jimi over the past few months.
"He was the kind of person that people call salt of the earth. He did not have any airs and graces and was not giving the money to gain publicity or to boast about his success, but just because he wanted to make a difference."
Ms Greenfield said Mr Heselden, who had humble beginnings in the Halton Moor area of Leeds after leaving school at 15 and working down the local pits, was keen to support local issues and when asked why he gave, replied: "I have done well in business and feel a duty to put something back and it makes me feel good to know I can help other people."
He brought hundreds of jobs to the Leeds area with the revolutionary protection baskets made by Hesco Bastion since 1990.
The "concertainer" units have been used to protect soldiers in every major conflict since the first Gulf War and is seen as one of the UK's most successful defence exports.
They are also used for a range of non-military functions including flood management and erosion control.
Bryn Parry, chief executive and co-founder of Help for Heroes, called Mr Heselden the organisation's "greatest benefactor" and added: "Jimi has been supporting Help for Heroes since September 2008 and was personally committed to giving the best support to 'the blokes' - the men and women of the armed forces.
"His support was unassuming but very effective and he shared in many of our projects and fundraising events, most recently the Heroes Concert."
Mr Heselden struck the deal to buy Segway in December last year. The firm was started by inventor Dean Kamen in 1999 after he developed the electric two-wheeled, self-balancing vehicle.
The Leeds tycoon had a fortune reported to be £166 million, making him one of the 400 richest people in the UK.
A spokesman for West Yorkshire Police today confirmed Mr Heselden was pronounced dead yesterday after being pulled from the river.
He added the incident is not believed to be suspicious and the coroner has been informed.
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