The WS Group has annual revenue of around £100m and has 650 employees.
Worldstores is an online retailer of 500,000 products for the home and garden. Achica is a members-only online store offering furniture, homewares and accessories. Kiddicare is a multichannel retailer, selling nursery supplies.
Dunelm is paying £8.5m for WS Group, but plans to spend £15m on the business.
Dunelm chief executive officer John Browett said: "We are excited by this opportunity to accelerate the growth of our internet operation, more than doubling its size, and enhancing our position as the destination homewares retailer in the UK, both online and offline.
"Between the store network, broad product range and strong brand that Dunelm has built and Worldstores' extensive homewares and furniture offer and unique platform for next day delivery and flash sales, we will strengthen our leading position as the UK's Home of Homes."
WS Group is expected to have trading losses of between £5m and £10m in the financial year to the end of June 2017, but Dunelm believes the business will at least break even by the end of June 2018.
Creditors such as garden furniture suppliers do not know if they will be paid their debts.