Mrs Paterson, 63, was found near the family home, between Overton and St Martin’s, in the early hours of this morning. Her death is not being treated as suspicious.
Mr Paterson described his wife, who held one of Britain’s most important sporting positions as chairman of Aintree Racecourse, as a “wonderful, caring wife, mother and grandmother”.
He said: “It is with great sadness that I must inform you that my wife, Rose, has been found dead at our family home in Shropshire.
“Rose and I were married for 40 happy years. She was a wonderful, caring wife, mother and grandmother. Her death has come as a terrible shock to us all.”
Mrs Paterson was found dead in woodland at the family's countryside farmhouse between Overton and St Martins.
She and Mr Paterson have three children, Felix, Ned and Evie.
Downing Street said Prime Minister Boris Johnson had offered his condolences.
A spokesman said: “His thoughts and every sympathy are with Owen, his children and grandchildren at this difficult time.”
Mr Paterson has been the MP for North Shropshire since 1997.
Steve Charmley, chairman of North Shropshire Conservative Association, said Mr Paterson had told him of the “devastating” news in a phone call this morning.
He described Mrs Paterson as a “fantastic person” who had forged an incredibly successful career, while also being the rock behind her husband’s political life.
He said: “I had known Rose for 10 or 15 years and I always found her to be a very grounded and friendly person. She was very supportive of Owen and the Conservative Party’s North Shropshire Association.
"She had a vast knowledge of the horse racing world. That was her passion, horses were very much a key part of her life.
“In a male dominated sporting environment it is no small achievement to take on the role she did.”
He added: “She was a real rock behind Owen. Through his time as Northern Ireland Secretary when they had body guards following them everywhere, through the tribulations of political life, it won’t be the same without Rose by his side.”
Anna Turner, Lord Lieutenant of Shropshire, described Mrs Paterson as “loved and universally respected”.
She said: “Rose was a very good friend and Deputy Lieutenant in Shropshire, we will truly miss her. She was loved and universally respected for being hugely intelligent and hard working but above all tactful and kind to everyone she came across in work and play.
“She and Owen set an example of how young love can be enduring, they met at university and 40 years later were still very happy and proud of their lovely family. I shall miss her sound advice and generous nature.”
Writing on Twitter Dido Harding, chairman of NHS Improvement, said: “Incredibly sad news. Sending love and condolences to Owen Paterson and family and all at Aintree Races. She will be much missed by all of us.”
Sandy Dudgeon, Senior Steward of The Jockey Club of which Mrs Paterson was also appointed a steward last year, said: “This is tragic news and our thoughts go out to Rose’s husband Owen and all members of her family.
"Rose was a wonderful person and involved in so many aspects of our sport. She was a skilled chairman at Aintree, a valued member of our Board of Stewards and headed up our Horse Welfare Group. She also enjoyed participating at grassroots level over many years.
“We appreciated her contribution very much and my fellow Stewards and I looked forward to hearing her sound views on a subject, where she was always sensitive to the best course of action for racing. She will be missed greatly for the person she was.”
A spokesman for West Mercia Police said: “We can confirm the body of a woman has been found in woodland near Pant Lane in Sodylt in Ellesmere.
"The death is currently being treated as unexplained, however at this stage there is believed to be no third party involvement.”