The 31-year-old singer-songwriter, famous for being the frontman in Irish band The Script, won his seat on the BBC talent show over Will Young.
"I have absolutely no idea how I managed to talk my way into it," he told Fabulous magazine.
"I'd interviewed for the position and been called back, but I heard that people like Mary J Blige were also in the running. I knew Will Young was the favourite.
"As far as I was aware there was a lot of hearsay and rumour and I didn't know anything for sure. But I was so thrilled to get the job."
The 'For The First Time' singer, who judges alongside Sir Tom Jones, Jessie J and will.i.am, also revealed that The Voice's success has increased his popularity.
"After the show went out I had 200 marriage proposals in two days," he recalled. "Crazy stuff. And I get a lot of girls tweeting the same message over and over asking me to follow them, which is a bit like someone constantly ringing your doorbell.
"I'm loving it though. I see it as a bit of fun unless it starts getting stalkerish. My mother checks my Twitter, and I wouldn't like her to see what people have said they'd like to do to me."
However, O'Donoghue insisted: "I never wanted to be famous for being famous. I wanted to be known for my music.
"But we've been looking for a project that would help get our personalities across for quite a while and this was the best way forward. Now's the time to go balls to the wall."
> Danny O'Donoghue: 'I tease Tom Jones over age'