The collaboration features on Womack's upcoming album The Bravest Man In The Universe, which is released via XL Recordings on June 11 in the UK and the following day in the US.
Talking earlier this year about working with Del Rey, Womack said: "She's one of a kind. I've never sung with a girl like that before."
The Bravest Man In The Universe is Womack's first studio album for 18 years and also features a song produced by Damon Albarn.
Del Rey this year released her debut album Born to Die.
In 2010, Womack featured on 'Stylo', the lead single from Albarn's Gorillaz album Plastic Beach.
Womack's friend Bootsy Collins confirmed earlier this year that the singer had been diagnosed with colon cancer.