Eugenie and husband Jack Brooksbank are expecting the new addition to their family - a brother or sister for their son August - in the summer.
Buckingham Palace said the royal family was "delighted" and that August was "very much" looking forward to becoming a big brother.
Eugenie shared a family photograph of him embracing her and kissing her bump to announce the news.
Eugenie wrote: "We're so excited to share that there will be a new addition to our family this summer."
The baby will be the third grandchild for Eugenie’s parents Prince Andrew and Sarah Ferguson. Eugenie’s sister Princess Beatrice welcomed her first child, Sienna, in September 2021.
A Buckingham Palace spokesperson said: "Princess Eugenie and Mr Jack Brooksbank are pleased to announce they are expecting their second child this summer.
"The family are delighted and August is very much looking forward to being a big brother."
The baby will be born 13th in line to the throne and will be a Miss or Master.
He or she will be the first of the Queen's great-grandchildren to be born since her death, and will arrive in the King's coronation year.
August Philip Hawke Brooksbank was born at the exclusive Portland Hospital in central London on February 9 2021.
He made an appearance at the Platinum Jubilee pageant celebrations last year wearing a union flag jumper as Eugenie bounced him up and down on her knee as they sat in the royal box.
In an interview at the World Economic Forum in Davos with Reuters IMPACT on Tuesday, Eugenie said her son was “going to be an activist from two years old” and spoke of her own attempts to stop using plastic at home.
Princess Eugenie and Jack Brooksbank - In pictures
Eugenie and Mr Brooksbank wed in a glittering ceremony in the gothic surroundings of St George’s Chapel, Windsor Castle, in front of royal and celebrity guests in October 2018.
The princess, the daughter of the Duke of York and Sarah, Duchess of York, is close to her cousin the Duke of Sussex, whose biography caused ructions this month when he laid bare his fraught relationships with the King and the Prince of Wales.
Mr Brooksbank, 36, has worked as a European brand director of Casamigos Tequila, co-founded by the actor George Clooney.
He met Eugenie through mutual friends while on a ski trip to Verbier.
Eugenie, 32, is a director at the contemporary art gallery Hauser & Wirth in London.
She is patron of several charities including the Elephant Family, the Teenage Cancer Trust, the Coronet Theatre and the European School of Osteopathy, and also founded the Anti-Slavery Collective charity.