The X Factor judge told Marie Claire that she struggled to achieve success in the UK because of her sister's popularity.
"When I first came over, it was hard because it was Kyliemania," she confessed. "She was this cute little thing and I was the fat, ugly sister.
"Can you imagine for years being asked what it’s like to be Kylie's sister?"
She added: "I guess it's my turn now to enjoy what is going right."
Dannii Minogue 'ignored Kylie comparisons'
Dannii Minogue has said that the success of her sister Kylie's career never made her "jealous".
According to the Daily Mail, the X Factor judge and popstar reveals in her autobiography My Story that press comparisons between the two siblings did not affect the pair's relationship or the "love and support" that they gave each other.
Minogue wrote: "Ever since I arrived in the UK in 1991, the media have pitted us against one another, first favouring my supposed 'cooler, darker' image over Kylie's bubblegum sweetness, then turning on me with a deluge of unflattering comparisons.
"Never mind that Dannii has had ten Top 10 records - Kylie has had 20! Never mind that Dannii's album has gone gold - Kylie's has gone platinum! Less success was no success at all as far as my critics were concerned. As much as it broke my heart at times, it never made me any less proud and supportive of my sister, and I received the same love and support from her."
The 38-year-old also said that she never compared her own career to Kylie's, adding: "The truth is I never felt as if I was competing with my sister. Although I got very tired of the constant comparisons, it wasn't because I was jealous. I think all the Dannii-bashing headlines often hurt Kylie more than they hurt me."
My Story is published on September 30.
