The couple met during the fifth series of ITV reality dating show Love Island in the summer of 2019. They came in second place, behind Greg O’Shea and Amber Gill.
They welcomed their first child, a daughter named Bambi, in January.
Hague - who has 8 million Instagram followers - posted a video of the romantic moment onto her page on Sunday.
In the video, Hague - who is wearing a strapless jumpsuit - can be seen arriving in a mountainous seaside location where she sees Fury holding their daughter Bambi. There are also huge bunches of flowers and rose petals scattered around.
Looking emotional, the 24-year-old influencer picks up her child as Fury, 24, gets down on one knee to propose.
The professional fighter and Hague then embrace and smile at each other.
Hague captioned the post saying “Forever. 23/07/23” along with emojis of a ring and a crying face.
The couple were congratulated by celebrities including Olivia Bowen, Sophie Habboo and Olivia Attwood.
Underneath Hague’s post, Bowen wrote: “Ahhhhhhh my goodness congratulations gorgeous people xxxxxxx.”
Gemma Collins wrote: “So happy for you congratulations.”
Maya Jama, who recently took over the show’s hosting duties from Laura Whitmore, said: “WE LOVE TO SEE IT! Congratulations you cuteys.”
Just a week ago, the couple sparked engagement rumours after Fury made a surprise visit to see her in France, where she was on a work trip. They went to Disneyland Paris and Hague wrote in the caption for her post about the surprise: “When you wish upon a star.”
Some fans are assuming the couple will have a Disney-themed wedding. Hague is a known lover of Disney - even naming their daughter Bambi after the 1942 Disney animated film of the same name.