The 920 million pound ($1.22 billion) float would value the firm at 4.5 billion pounds and see it list at least 20% of its stock. The company will also sell some existing shares.
Blackrock, Henderson Global Investors and funds managed by Merian and the Qatar Investment Authority have agreed to buy 565 million pounds of the shares on offer.
Admission to the stock exchange is expected later this month.
THG operates retail brands including Lookfantastic and skincare group ESPA and has said it has benefited from an online shopping boom since government lockdowns were introduced to control the spread of COVID-19.
The Hut IPO is expected to be the biggest IPO of a British company since the government floated the shares of its Royal Mail postal service in 2013.
International companies including Chine Pacific Insurance Co. and Russian resource company EN+ ENPLI.RTS raised potentially more with their global depositary receipts.
CitiGroup, JP Morgan, Barclays and Goldman Sachs are acting as joint global co-ordinators, while HSBC, Jefferies and Numis are joint bookrunners. NM Rothschild & Sons is sole financial adviser to the company.
(Reporting by Iain Withers, editing by Sinead Cruise)