The statement said Ruth had died aged 46 of the rare form of lung cancer she suffered from in her home country of Australia.
Strauss, a former England cricket captain, announced in early October he was standing down permanently as the national side's director of cricket following a period of compassionate leave.
Ruth was diagnosed with cancer during the Ashes in December 2017 and he took a break from his position earlier this year after she began a new course of treatment.
"It is with great sadness and immense grief that we have to announce that Ruth passed away today as a result of her rare lung cancer," read the statement issued by the England and Wales Cricket Board (ECB) on behalf of the Strauss family.
"Sam, Luca and I will miss her terribly.
"Anyone who has met Ruth will know how loving, caring and passionately protective she was of her family and it gives us huge comfort that she was in Australia, the land of her birth, surrounded by those who love her, in her final moments."
The Strauss family thanked the medical team who had treated her and said they would be helping others with the disease.
"Ruth desperately wanted to help those affected by this terrible disease," read the statement.
"We will be launching a foundation in due course to raise much needed funds to aid research and also to offer support to patients and their families."
First Published: December 29, 2018, 9:08 PM IST