Worldstores specialises in home and garden products, while Achica is a members-only online furniture store.
Dunelm is to buy the loss-making firm out of administration.
In total, WS Group has 650 employees and Dunelm said the move means that its online operation has more than doubled in size.
Dunelm boss 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."
Dunelm said it would pump £15m into WS Group as working capital and retain its management team.
WS Group is expected to turn a loss of "around £5-10m" this year, but Dunelm is forecasting that it will at least break even under its first full year of ownership.
Caroline Gulliver, analyst at broker Jefferies, said: " The deal gives Dunelm access to £100m of sales and £10m of operating synergies as Dunelm can harness Worldstores' technology and online expertise. We think this is a good deal for Dunelm."