The New Zealand retailer had $18 million in cash and equivalents as at June 4 after selling its neighbouring Harbour City Centre.
The rest of the proceeds went toward paying off $23.5 million in bank debt. Kirkcaldie will receive a final $4.75 million instalment on the sale in October.
Kirkcaldie shares surged as high as $2.29 after the David Jones announcement from $1.68 prior to the deal, having slumped to a record low $1.58 late last year. The stock last traded at $2.22.
Like many retailers, Kirkcaldie has come under pressure as bricks-and-mortar stores are forced to discount stock to compete with online rivals, and department stores in particular have struggled, including David Jones, which was taken over by South Africa's Woolworths Holdings and delisted from the ASX last year on falling sales and weak profitability.
David Jones will pay A$500,000 for the Kirkcaldie name and take over the lease of the Wellington site with the option to buy the retailer's assets for $500,000.
The transaction requires shareholder approval at a meeting expected at the end of June and needs Overseas Investment Office approval.
The department store will trade under its existing name until late January 2016. The David Jones rebranded store would open mid-2016.
Brierley first emerged as a substantial holder of Kirkcaldie in 2011 when the company's shares were seen trading at a discount to the value of the company's real estate, the Harbour City Building.
Around that time, former Brierley Investments chairman Selwyn Cushing and his son David Cushing lifted their family's stake in the retailer to 17.1 per cent and currently hold 19.5 per cent, according to the Companies Office.
The Cushings and Brierley are known for buying undervalued assets.