It continues: "You're sitting there like a dog with a seven-year itch ... And I think you've said enough for one motherf***ing night."
The musical duo's 13-track album is set to be released at the end of this week, on July 15.
It comes after Beck released a statement last month revealing the reason behind the album's title.
"We would joke about how we felt 18 again so that just became the album title, too," he said.
The album contains covers of The Velvet Underground's Venus In Furs, the Everly Brothers' ballad Let It Be Me and Marvin Gaye's soul classic What's Going On. There also are versions of Davy Spillane's Midnight Walker and two songs from the Beach Boys' masterpiece Pet Sounds - Caroline, No and Don't Talk (Put Your Head On My Shoulder).
Depp's latest career move comes one month after a jury found the Pirates of the Caribbean star should be awarded the partial sum of US$15 million (NZ$23.1m) in damages.
Depp was initially seeking US$50m after Heard implied, in a 2018 Washington Post op-ed, that he abused her. Although she did not name him, he claims her allegations are false and cost him lucrative movie roles.
However, despite the win, the jury also found in favour of Heard, who countersued Depp for US$100m.
Heard claimed she was defamed by Depp's lawyer when he called her abuse allegations a hoax. The jury agreed to a lesser degree, awarding her just US$2m of the hefty sum first requested in damages.
Depp was not present to hear the verdict in his defamation case - instead, he was in the UK touring with Beck, with sources claiming he was absent due to "previously scheduled work commitments".