And it immediately pledged to double Giddings' 30-strong workforce, stating it will introduce additional shifts to double the mill's sawn capacity to more than 60,000 cubic metres.
Berwickshire-based BSW, which has four of its six UK mills in Scotland, said the acquisition builds on its footprint in England and Wales by adding to its sites in Cumbria and Powys, Wales.
BSW chief executive Tony Hackney, who joined the board of RF Giddings as a non-executive director to help steer the deal through, said: "The Giddings mill is part of a growth phase BSW is going through.
"We have had potential acquisition targets but we have also growth organically. The Southampton location, being on the edge of the New Forest, is a great location for us to serve the south-east market, which is only an hour and 20 minutes away.
"It's a fairly new mill, with a good team down there and gives BSW potential for furthering its geographical reach in the UK and Europe."
RF Giddings, a fourth generation family business, produces materials for the fencing, pallet and construction industries.
BSW hailed the company's reputation and supply network as key drivers of the acquisition. It will retain Giddings' existing relationship with sales agent Taylor Maxwell Timber to ensure continuity of supply for existing customers, which will now be able to buy timber from other BSW sites.
The Giddings family will exit the business when the deal is formalised on August 1. Mr Hackney did not comment on any windfalls the shareholders will incur as a result of the deal, beyond stating the family had worked hard to secure their exit from the business.
He acknowledged the upturn in the UK construction sector as a factor behind the deal, insisting the recovery vindicated BSW's decision to invest between £80m and £100m to facilitate growth and make technical improvements to its products during the recession.
In addition to serving the UK it exports timber to China and North Africa, and also serves markets in Europe from its mill in Latvia. Not including Southampton, BSW has 1012 staff, with 700 in Scotland. It recently added 65 to its ranks across its sites in Dalbeattie and Cumbria by increasing shift capacity.
Mr Hackney said the firm remained on the look-out for further acquisitions.