The purchase price was not disclosed.
Telford-based Elements Europe has delivered more than 20,000 pods and volumetric modules over the past 10 years or so, primarily for hotels and student accommodation developments.
In the year to March 2019 Elements (Europe) Ltd made a pre-tax profit of £423,000 (2018: £790,000) as turnover fell to £23m, down from £40m the previous year.
With owners Mr & Mrs John Pickstock selling out control to GS E&C, Elements Europe directors Kevin Arthur, Terry Lunt, Robin Jones and chief executive Simon Undxerwood have been replaced on the board by Jong Hwa Lee, Do Young Kim and Yoon-Hong Huh.
In addition to hotels and student accommodation, Elements Europe has delivered more than 500 apartments and homes in recent years including two 23-storey residential towers in Greenwich and Croydon.
GS E&C, an £8bn turnover enterprise, plans to build a new facility in the Midlands and open further factories throughout the UK to scale up capacity. Elements Europe will also pitch for more turnkey projects, from concept to completion, and is seeking joint venture opportunities.
Yoon-Hong Huh, president of GS E&C, said: “We are excited to invest into Elements Europe, they have 15 years of experience and a track record of delivery. Added to that, they have built a successful platform and invested heavily into the development of their products, technology, design processes and people in order to support rapid expansion plans.
"We are confident that our investment in the business will enable substantial growth in Elements Europe's offering, maintaining and expanding their strong market position."
Elements Europe chief executive Simon Underwood said: "The additional investment into our company will transform the capacity of our business and comes at a time when the market is in need of increased output in this sector. Our volumetric module and pod solutions have never been in more demand. GS E&C brings substantial strength and an ongoing, long-term commitment to invest into the business to meet this demand."