The 32-year-old former boyband member said he finally got down on one knee after his three-year-old son, Beau, asked him if they were married.
The couple, who have been together for almost 13 years, are expecting a second little boy later this year.
Speaking to UK magazine, Hello!, Jones said: 'Beau asked me a little while back, 'Are you and Mummy married?' And that got me thinking.
'I come from a family where my parents weren't married and I wanted to give Beau a proper family set-up.'
Bunton, 35, added: 'Beau was sitting on my lap when Jade proposed, so he was very much involved in it all. But he's a little bit confused, because he said, 'So you're married now?’
'I guess there was so much hugging and screaming when Jade asked me to marry him, Beau thought that was it – he hasn't quite grasped we've still got that to come.'