"We are very happy for them," said Sophie's mother Katharine from her home in Edinburgh. "It's a really fabulous day. It's only just been announced so we don't know any more but it's lovely news."
Patrick and Katharine Hunter spoke about Sophie and Benedict's engagement news
Sophie's younger brother Patrick, 30, also shared his joy saying: "We're all very happy for Soph - it's really exciting."
According to the Hunter family no date or location have been set for 36-year-old Sophie and 38-year-old Benedict's big day yet.
Ever the traditionalist, Benedict is said to have flown to Edinburgh to ask Katharine's permission to marry her daughter, a gesture which is in keeping with formal way the engagement was announced.
Benedict and Sophie at the French Open in June
A small notice in The Times newspaper read: "Mr B. T. Cumberbatch and Miss S. I. Hunter. The engagement is announced between Benedict, son of Wanda and Timothy Cumberbatch of London and Sophie, daughter of Katharine Hunter of Edinburgh and Charles Hunter."
London-born Benedict has been dating Oxford graduate Sophie since at least June when they were seen at the French Open together, although sightings of them as a couple are extremely rare. The pair have a friendship dating back several years, however, when they appeared in the 2009 film Burlesque Fairytales together.
The couple's engagement was announced in The Times
Benedict has been keen to settle down for some time and previously spoke about how he had envisaged getting married and building a relationship that would stand the test of time.
"It's a wonderful thing to get married young and become a father," he told Elle Japan last year. "I used to think that I'd get married by my mid-thirties and have children. But now I think I can wait. I'm no longer in a hurry to get married. I would like to first get to know the partner and build a trusting relationship before making the commitment."