Scottish Government business, innovation and energy minister Paul Wheelhouse revealed details of that development, as well as others planned in the town, on Monday.
The others include the development of four units at Galalaw Industrial Estate and the upgrading of existing facilities in Tower Mill.
The investment confirmed this week, following the launch by Scottish Borders Council of its Hawick action plan last year, is expected to create 55 jobs.
The cash is part of a £10m local economic development capital grant fund also supporting businesses in North Ayrshire, Clackmannanshire and Fife.
Mr Wheelhouse, a Scottish National Party list MSP for South Scotland, said: “The business incubator in the former Almstrong’s building will give new and rapidly-developing companies the opportunity to come together and grow.
“The new and upgraded business infrastructure in and around Hawick will encourage entrepreneurs, generate start-ups and ensure that the region can meet all the business needs that expanding companies may have.
“This will boost the economy in the South of Scotland, creating up to 55 jobs, and will let local businesses build upon the reputation for innovation and hard work for which they are renowned.”
The project is the first piece of council business for Mid Berwickshire councillor Mark Rowley, now the authority’s executive member for business and economic development.
He told us: “These projects will not only provide new job opportunities in Hawick but will hopefully act as a catalyst for further property redevelopment and inward investment in the town in the future.
“Redeveloping the former Almstrong’s building will deliver new, small office units suitable for start-up firms and existing businesses in the town centre and will also bring life back to a building which has been empty and derelict for many years.”
The Almstrong’s site will be developed on a phased basis, with the front fitted out as incubator units with meeting rooms and small café area.
The Teviot Crescent section, currently within the flood zone area, will be renovated but not fitted out internally during the initial phase.
Depending on funding availability, the fit-out could progress once the forthcoming Hawick flood protection scheme work has been completed. That could also include large business units or residential development, depending on need at the time.
However, not everyone is enthusiastic about the plans.
At Monday night’s Hawick Community Council meeting, honorary provost Watson McAteer said: “First of all, we have to welcome that £3.6m is coming into Hawick – that’s a given – but if I’m being honest, I worry about the ambition of the project.
“I think that most people would have liked to see Almstrong’s knocked down to create a thoroughfare from Teviot Road to join up to Commercial Road. I think I would have probably preferred that.”
He added: “Getting the £3.6m, I’m not diminishing that at all, and we will all have different views.
“My concern is that it doesn’t feel ambitious enough.”
“What we have got is the result of the previous administration.”
It is proposed that a link between High Street and riverside area is established as part of the development.
That would be anticipated to provide 17 business incubator units and up to 25 jobs.
The estimated cost of the Almstrong’s development is £2.6m.
A further £1m is to be spent elsewhere in Hawick, creating another 30 jobs.