He/I will keep this secret. Although the idea of keeping one’s mouth tightly shut is much older and sealing up someone else’s lips dates from the late 1700s, this particular expression became current only in the early twentieth century. It was much repeated by Prime Minister Stanley Baldwin when asked about the rumored abdication of King Edward VIII, who wished to (and eventually did) marry a divorced American, Wallis Simpson. See also mum's the word.