Her debut on the programme - along with Ricky Wilson from Kaiser Chiefs - helped the first show of the series to an average audience of 8.4 million viewers, well above the 6.2 million who tuned in last year.
It also thrashed ITV's celebrity diving show Splash! - which went head to head with the BBC1 show - with an audience of 3.7 million, according to overnight ratings.
This year the BBC has brought forward The Voice for its third series, after previous runs kicked off around Easter, putting it up against shows such as Britain's Got Talent.
Saturday night's launch was level with the audience for the first series in 2012 which had a strong start, but saw figures drop sharply after the early rounds featuring the spinning chairs.
Minogue and Wilson were drafted in after Jessie J and Danny O'Donoghue stepped down from the show. Sir Tom Jones and Will.i.am continue on the panel of coaches.
The audience for Splash was one of the smallest it has brought in since the programme launched early last year.
The controller of BBC1 Charlotte Moore was delighted with the start made by the new series.
She said: "BBC1 continues its start to the year in excellent form with the return of The Voice peaking at a huge 10.6 million last night. As we hoped our new line-up is clearly connecting with audiences."