The pair were so impressed by the singer's take on 'Get Here' last month that they requested she sing at their upcoming nuptials, The Sun reports.
"I've been addicted to The Voice. It's amazing, isn't it?" O'Dowd said.
"Ruth is definitely our favourite, that girl can really, really sing.
"Dawn has picked out a special song she wants for the wedding when she is walking down the aisle. I can't say what as it's a surprise for the day but it'll need a big voice to sing it."
The couple plan to marry in August after getting engaged last year.
Digital Spy readers voted Ruth Brown their favourite performer following The Voice UK's first live show.
Watch Team Jessie J discuss The Voice UK below: