The investment company, which listed on London’s main market today, will pay up to US$23.75mln for the stake.
The catalogue was one of the eight pipeline catalogues flagged in the company's pre-flotation prospectus, and comprises 302 songs in total, including 25 Billboard top 10 songs, four Grammy Award-winning songs and songs performed by global recording artists such as Justin Bieber, Beyoncé, Rihanna and Jay-Z.
Songs in the catalogue include the Number one singles: "Umbrella", which was number 1 in more than 20 countries; "Single Ladies (Put a Ring on It)", the 2010 Grammy Award Song of the Year; and the multi-platinum Touch My Body by Mariah Carey.
"It's critical for us to set the highest standards with our first acquisition,” said Merck Mercuriadis, the founder of Hipgnosis Songs.
“It's an honour for this to not only be our first order of business but also to welcome Dream to our advisory board. He is a catalyst on so many levels and a big part of our future," Mercuriadis said.
Shares in Hipgnosis, which floated at 105p, were unchanged at 103.5p following the announcement.
The investment company focused on song royalties saw strong demand for its shares in a share placing at the end of June, raising £200mln before expenses.
Hipgnosis plans to use the funds to acquire a diversified portfolio of songs featuring hits from each of the past five decades, including more than 10 number one hit songs in the UK and US.
The company was founded by Merck Murcuriadis, the former manager of internationally renowned acts such as Elton John, Guns’n’Roses, Iron Maiden and Beyoncé.
The trust's investment adviser is The Family (Music) Limited; its advisory board includes legendary Chic guitarist and record producer, Nile Rodgers.