LONDON — Of all the glad tidings that Prime Minister Boris Johnson promised would flow from Brexit, one of the most far-fetched was a baby boom. But at least in his own case, Mr. Johnson has actually delivered on that pledge.

The 55-year-old prime minister and his partner, Carrie Symonds, 31, said on Saturday that they had become engaged and were expecting a child in early summer. A spokeswoman for the couple told the BBC they were “very pleased” to share the news.

Mr. Johnson will be the first prime minister since Tony Blair to have a child while living in 10 Downing Street. Mr. Blair and his wife, Cherie, had a son, Leo, while there in 2000. In 2010, three months after becoming prime minister, David Cameron and his wife, Samantha, had a daughter, Florence, while on a family vacation in Cornwall.

Mr. Johnson and Ms. Symonds were the first unmarried couple ever to move into the prime minister’s residence. The child will be the first for Ms. Symonds, a former communications chief for Mr. Johnson’s Conservative Party.