It follows the announcement last December that it had entered into binding agreements to purchase the businesses.
The agreement will see nearly 300 people from Bassetts, DHS, and Neville Lumb joining the Wolseley UK business.
As with the previous acquisitions, it will be a seamless transition; all outlets will operate as normal and there will be no change for customers.
Simon Oakland, chief execuvite at Wolseley, said: “The completion of the acquisition of Bassetts, DHS, and Neville Lumb marks a very exciting chapter for the business, our customers, and our colleagues, both existing and new.”