The couple, who tied the knot on Friday 4 July, can be seen dancing to Tom Odell's live performance of Lana Del Rey's hit 'Video Games'.
Radio 1 host Fearne said: "I will dream of this moment for ever. Tom Odell singing Video Games live with a choir for our first dance #4714."
In the sweet video, the couple can be seen holding each other at the waist before sharing a kiss on the dance floor.
Fearne, who got engaged to Jesse in December last year, planned her nuptials in secret and surprised fans in July when she was spotted leaving London's Ritz hotel in a gorgeous wedding gown by bespoke designer Maggie Cook.
Last month, Fearne shared a photo of herself and Jesse during their first dance, describing it as a "magical moment".
Just two weeks ago (26 July), newlywed Fearne marked three weeks of married life with a sweet photo of her and Jesse kissing in front of guests. She said at the time: "I've now been Mrs Wood for 3 weeks."
Denise Van Outen, Gok Wan, Dermot O'Leary, McBusted, Celebrity Juice host Leigh Francis and Fearne's best friend Holly Willoughby were among the guests at the wedding.
Fearne and Jesse - who is the son of The Rolling Stones' Ronnie Wood - have been dating since 2011. The couple welcomed their first child together, one-year-old son Rex, last February.
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