The Welsh Rugby star gave his final rose to the 24-year-old model during a romantic trip to St Lucia, rejecting 29-year-old singer Layla Manoochehri.
Henson told Barrow: "I've been looking for a long-term relationship. Someone I can give 100% to and will get that back... Carianne, you're the one.
"I feel so lucky to have found you, you're so unique. Please give me the opportunity to make you feel special. Let me be your best friend and give me the opportunity to make you happy for the rest of you life."
The new couple then professed their love for each other, with Barrow telling him: "I want to be with you forever."
The beginning of Henson's new romance attracted 1.34m viewers on Channel 5 last night (October 28). Barrow beat out 24 other women to become Henson's new girlfriend.
Henson told Digital Spy in August that he hoped to find a "genuine" romance on The Bachelor.
Ex-Big Brother housemate Imogen Thomas has reportedly been approached for upcoming spinoff The Bachelorette.