The song is an electropop track, which features instrumentation of synthesizers and keyboards, whilst the lyrics talk about the thrills of a new romance.

"Giving You Up" received mixed reviews from music critics, who complimented Minogue's vocals but dismissed the production and composition.

It peaked inside the top ten in both Australia and the United Kingdom, and also charted in Austria, Belgium, Denmark, and Finland.

Alex and Martin commissioned the accompanying music video for the single, which shows Minogue as a giantess and walking around the streets of London.

[2] The month after, it was announced that she would be releasing a greatest hits album, titled Ultimate Kylie, containing two new tracks,[3] being "I Believe in You" and "Giving You Up";[4] Jake Shears and Babydaddy were in charge of the production of the former, whilst the latter was produced by Brian Higgins and Xenomania.

A separate compilation DVD with the same name, containing several music videos by the singer, was also released to coincide with the distribution of the album.

[9][10] All formats feature the B-side "Made of Glass", which was written by Minogue and Xenomania during the recording sessions for Ultimate Kylie in 2004.

[15] Pitchfork reviewer Nick Sylvester called the song "a return to big sound Fever electro, but with subtler production: all the hacksaw synth is pushed back and sanded off, so Kylie's head voice doesn't have to go through eight additional filters to compete with the bristle".

[22] The song reached the top forty in other territories in Europe, including Finland, Belgium, Germany, Netherlands, and Switzerland.

[27] The video features Minogue as a 17-foot tall, vampy, blonde giantess roaming through the streets and clubs of London at night.