Lady Lavinia Nourse was married to Sir Martin Nourse who died in 2017, aged 85.
The 77-year-old, of Newmarket in Suffolk, described the allegations, which relate to a single male complainant, as a “complete fantasy”.
Jurors at Peterborough’s Nightingale court took less than five hours of deliberation to find her not guilty of all 17 charges.
She was cleared of five counts of indecently assaulting a boy under the age of 12, and was also found not guilty of 12 counts of indecency with a child.
The defendant, who stood beside her legal team, wiped away tears as the verdicts were returned.
Giving her evidence earlier in the trial, Lady Lavinia had told jurors the complainant was “obviously after money” and that the allegations were “completely untrue”.
When she was interviewed by police in 2019 she said she was “shocked” when she was first told of the accusations against her.
“To me this is a complete fantasy,” she said.
“I don’t know what he’s talking about.”
Later in the interview, she said: “I’m finding this very difficult.
“It really is cloud cuckooland.”
Jennifer Knight QC, prosecuting, earlier told the trial the boy “tried to bury away the memories” of alleged abuse but that, years later, after he got married and had children, he “became increasingly troubled by his recollection” and told his wife.
A number of Lady Lavinia’s high-profile friends were called as character witnesses as part of her defence case.
Sir Malcolm, who served as a cabinet member under Margaret Thatcher and John Major, said Lady Lavinia was “very sociable and very gregarious”.
Dame Mary, the wife of Lord Jeffrey Archer and chairman of the Science Museum, said she and Lady Lavinia were “both completely cat mad” and she described the defendant as “one of my closest friends”.
After Lady Lavinia was cleared of all counts she sat back down, slumped forward and rested her head on the desk in front of her with her arms folded around it.
As she left the court she told reporters: “It’s a happy result.
“Finally some good news.”