Soames, born Mary Spencer-Churchill, was the youngest daughter of former British Prime Minister Churchill and his wife, Clementine.
She served in the auxiliary territorial service during World War II during the same time her father served as premier.
She married prominent conservative politician Christopher Soames in 1947 and later became Lady Mary Soames.
Prime Minister David Cameron said he "felt privileged to know her."
She was "a wonderful, warm-hearted woman who could always put others at ease," he said.
"In the week of the 70th anniversary of D-Day, we remember that she served her country in World War II and was an eye-witness to some of the most important moments in our recent history as she accompanied her father to key conferences," Cameron added. "My thoughts are with her family, who can take pride in her distinguished life."
Soames' son, Nicholas Soames, is a conservative MP and former minister.
"She was a truly remarkable and extraordinary woman, who led a very distinguished life," he said of his mother.