A previous bid competition to deliver the Box Encapsulation Plant Product Store and Direct Import Facility was abandoned in 2013 after failing to attract sufficient interest.
M+W Group, which is based in Stuttgart, will use local Cumbrian firm James Fisher & Sons as it civils contractor.
The project to encapsulate intermediate level waste in cement for above ground storage at the site has suffered a chequered history.
A joint venture between Jacobs, Atkins and Carillion first started work on the project back in 1997.
But the job was halted in 2002, due to technical uncertainties, and the partially completed on-site facilities put in mothballs.
After a project rethink in 2010 Balfour Beatty, in joint venture with Babcock, secured the early contractor engagement phase of the Box Encapsulation Plant Product Store and Comprehensive Import Export Facility, as the waste store project became known.
The project was then valued at around £250m.
Following another strategic review in the face of rising costs, Sellafield bosses decided to cancel this planned expansion and replace it with an alternative simpler facility known as the BEPPS and Direct Import Facility, which formally went to prequalification stage before being cancelled because of insufficient interest.