Administrator James Tickell, of Portland Business and Financial Solutions, was appointed to the Southampton-based business on 5 May.
A spokeswoman for the insolvency practioner said: "The company has ceased to trade, but we have managed to sell its database and telephone numbers.
"Unfortunately, all 31 staff have had to be made redundant; 15 initially and the remaining 16 after we were appointed."
According to the administrator, WBF collapsed because it was unable to afford the renewal of the lease on the premises that it had occupied for the past 30 years.
"There was a figure of £200,000 needed to put the premise right once the lease was up and the company couldn't commit to that sort of liability," the spokeswoman explained. She added that the £2.4m turnover company had been decreasing in turnover.
She said that the administrator had looked for a buyer and approached several trade creditors and suppliers. As a result, business forms printer DCL Print acquired the company's database, records and machinery, which included a Didde MVP XF five-colour reel-to-sheet press.
Simon Smode, DCL Print group managing director, said: "We've known Weston Business Forms for years and sadly, due to the volume decline, it has fallen into administration."
The Crawley-based business has also taken on four of the company's staff.
"As a business forms printers, this purchase will complement our current business. We will also continue to run the sales operations from offices in Southampton," said Smode.
"We have acquired a number of companies in the past and will continue to seek opportunities for further acquisitions."
DCL Print is located in Crawley and it has 40 staff and a turnover of £3.5m. Last year, it moved into label and card printing after acquiring a number of assets from Centrereed's administrator.