At the time Ben Stokes condemned The Sun for running the story calling the newspaper's decision as "utterly disgusting" and the "lowest form of journalism" in a social media post.
"The decision to publish this article was a decision to expose, and to profit from exposing intensely private and painful matters within our family," said Deborah Stokes.
"The suffering caused to our family by the publication of this article is something we cannot forgive.
"Ben and I can take no pleasure in concluding this settlement with The Sun.
"We can only hope that our actions in holding the paper to account will leave a lasting mark, and one that will contribute to prevent other families from having to suffer the same pain as was inflicted on our family by this article."
The Sun told the BBC at the time it had received the co-operation of a family member.
The Sun's statement read: "On 17 September 2019 we published a story titled 'Tragedy that Haunts Stokes' Family' which described a tragic incident that had occurred to Deborah Stokes, the mother of Ben Stokes, in New Zealand in 1988. The article caused great distress to the Stokes family, and especially to Deborah Stokes. We should not have published the article. We apologise to Deborah and Ben Stokes. We have agreed to pay them damages and their legal costs."
