The charity said the premises at Audley Court were no longer suitable for its service and that it was working with veterans to find a more cost-effective location within the central region of the country.
Interim chief executive officer of Combat Stress, Jeff Harrison, added that the move would not affect the number of people receiving support in the Shropshire and Telford & Wrekin areas.
Set to be listed for sale on Monday, the site is expected to receive offers in the region of £1.5-£2 million.
It will still be operational until the move is complete, having also been used as a vaccination centre throughout the pandemic.
It comes after the charity ceased offering residential treatment at the facility in 2017, before announcing its plans to sell it last year.
Mr Harrison said the "ideal" location to move to would be somewhere between, Birmingham, Coventry and Leicester.
"We're trying to make all of our sites as accessible as possible and this new venue would cover all of the Midlands," he said.
"We're not looking to purchase, we're looking to rent. That's a significant change for the charity, as Audley Court was a big property which meant it was inflexible in terms of our financing.
"We're actively looking now so if we found something we'd move in relatively short term – that means months rather than weeks."
Throughout the pandemic the charity has focused on increasing its digital services and has run online and over-the-phone therapy.
Self-help guides published by the charity in November have been accessed more than 4,000 times.
Mr Harrison said: "There will always be people that need to see somebody and we'll be piloting in-person treatments again in August and starting them in September. This will include Audley Court until we find a more suitable location."
Due to funding cuts, Combat Stress ceased offering residential treatment in Newport in 2017 in order to continue the service in Scotland and South England. This left a large part of Audley Court redundant.
"At one point we had 28 bedrooms as well as all the treatment rooms unused, it was just too big," Mr Harrison said.
Nationally, Combat Stress has seen its referrals drop from 2,000 pre-Covid to 1,500, although the charity has shifted its focus to deal with veterans with the most complex mental health disorders who require more in-depth care.