The TV presenter, 37, revealed the happy news live on air during the Friday night episode of the show (6 February).
A beaming Alex gushed: "Thank you so much for all the lovely messages today."
She also took the opportunity to flash her sparkling ring at the cameras.
The stunning engagement ring is estimated to be worth £30,000, according to diamond expert Lewis Malka.
And, at the end of the episode, Charlie made a very brief appearance - much to Alex's protests!
She has been dating her New Zealand boyfriend, an insurance broker, for three years and is recently said to have bought a house with him.
Alex previously dated handsome TV presenter Steve Jones, with whom she co-hosts Comic Relief's Let's Dance.
The One Show's Chris Evans had already hinted Alex's engagement news earlier in the day on his Radio 2 Breakfast Show.
He said: "Tonight on The One Show there will be some news... [about] Alex Jones.
"All I'm saying, it's huge news... But for a girl it's probably like the second most exciting thing that could happen [and] it's happening to Alex."
Thanks for all your messages. We are thrilled! I was so nervous on that show but we're both so pleased to share the news with you all. Yay!— Alex Jones (@MissAlexjones) February 6, 2015
After making the exciting announcement live on air, Alex later thanked fans via Twitter.
She said: "Thanks for all your messages. We are thrilled! I was so nervous on that show but we're both so pleased to share the news with you all. Yay!"
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