The Huddersfield-based retailer says it will be moving into the Victoria Road building currently occupied by the Original Factory Shop, known as Tofs for short.
Tofs had already announced it will be closing after its management failed to come to an agreement with the landlord of the building.
Gerry Loughran, property director for Poundstretcher, said: “We saw the opportunity to take over the Original Factory Shop outlet and felt we can offer a fantastic shopping experience and great bargains on a range of branded goods to the people of Hawick.”
Poundstretcher, founded in 1981, has more than 400 stores nationwide, but none in the Borders since the closure of its Galashiels and Hawick High Street outlets a few years ago.
A worker at the town’s Tofs store said fellow employees were hoping they would be re-employed once the chain returns to the town.
They added: “It’s pretty awful being told you’re losing your job, particularly at this time of year, but this latest news offers some hope.”
Trading figures for the Original Factory Shop nationally show that revenue fell from £190.2m for the year to April 2017 to £183.2m last financial year.
The Burnley-based company announced that 32 of its 208 stores nationwide were to close in July.
At that time, Hawick’s was not among the outlets earmarked for the axe, but the 10 staff there were informed of the closure plans late last month.
The chain’s only other Borders branch is in Kelso.
A spokesman for Tofs said: “Unfortunately, we can confirm the Original Factory Shop’s store in Hawick is set to close.
“This is disappointing for Tofs, which had valued its role in the local Hawick community.
“It is too early to know the closing date. However it is most likely that the store will trade until early January.
“We tried really hard to come to a suitable agreement with the landlord, especially as this is a store that has been performing well and we are proud to be an integral part of the community.”