Senior, who is the daughter of current owner and chairman Richard Senior, will take over as managing director, with Yeung also becoming a director.
Richard Senior will continue to act as a consultant following his departure from the £4m-turnover, Scarborough-based business.
The assets and liabilities of the 70-staff business have been bought by Lawact 5, which will continue to trade as Duraweld, however Richard Senior will maintain ownership of the premises.
According to Hannah Senior, the company's new management will concentrate on improving the internet side of the business, making ordering easier for its customers.
She said: "We want to understand our customers better, make it easier for them to get quotes and generally add value to what we offer. Mark and I have both worked in online environments, which helps, but my Dad was always a huge supporter of online efforts."
Senior added that, having worked for large corporate businesses including Tesco, it was always her ambition to move into a more entrepreneurial, small environment. She joined her father's company around two years ago.
Other areas of improvement earmarked by the new team include improved customer service, reducing environmental impact and general cost savings.