The LEGO House (21037) kit will be launched just ahead of the grand opening of the visitor centre, which was designed by BIG for the company's hometown of Billund, Denmark. Ingels revealed a picture of the Lego kit on his Instagram account last week.
The 774-piece, 197-step kit replicates the stacked-block formation of the building and its brightly coloured terraces, which indicate different zones within the building. A block shaped like a giant lego brick crowns the building.
The kit is part of the Lego Architecture line, which also includes Frank Lloyd Wright's Guggenheim Museum and a set of monochrome building bricks designed to give architects the chance to create their own buildings.
The set will be sold exclusively at the Lego House, but 600 AFOLs – Adult Fans of Lego – will have a chance to snap up the kit on 22 September, when the centre will be hosting a special pre-opening event.
Plans for the visitor centre, which is designed to resembled a set of giant building blocks, were unveiled back in 2013, and work began the following year.
Ingels described the opportunity to design the building for the Danish toy company as "a childhood dream" in an interview with Dezeen in 2014.
"If BIG had been founded with the purpose of building only one single building, it would be the Lego House," said Ingels in a quote included in Lego's pamphlet for the kit.
The building’s location in Billund, where Lego was founded in 1932, puts it close to the Lego theme park.
It will include a mixture of free and paid-for attractions including a town square and a cafe where meals will be served in Lego brick-shaped lunchboxes by robots. Architectural photographer Iwan Baan posted a video of the service on his Instagram account.
"The building itself reflects what Lego play and the Lego values are all about," said Jesper Vilstrup, the manager of Lego House. "The Lego brick has been incorporated into the architecture in a simple but ingenious way, and visualises the systematic creativity that lies at the very core of all Lego play."
"Lego House is a manifestation of the very essence of the Lego idea. This will be an amazing place where Lego fans, their families and friends can experience – or re-experience – the playfulness of the Lego universe."
In the run-up to the official opening on 28 September, Lego has also released drone footage of the building nearing completion.
The Lego House was included in Dezeen's top 10 buildings to look forward to in 2017. It is one of several major products BIG is currently working on, including a pair of cactus-shaped towers beside a new IKEA store in Copenhagen and a yin-and-yang-shaped panda enclosure for the city's zoo.
Bajrke Ingels ranked second on the inaugural Dezeen Hot List, a guide to the most noteworthy figures in the architecture and design industries.