The Grade II*-listed building was built on St Mary Axe - now the site of Foster's Gherkin - in 1903, and was a splendid testament to Edwardian architecture.
English Heritage mothballed the surviving relics and, along with its mahogany, brass and bronze interior, the building's famous facade passed through a succession of antique and salvage dealers until, last year, two Estonian businessmen paid Kent salvage dealer Dennis Buggins £800,000 for the lot.
Heiti Haal and Eerik-Niiles Kross are now the proud owners of more than 1,000 tonnes of granite, plus the marble and interior fixings that make up the Old Baltic Exchange.
The first 50 containers of material have already landed at Estonia's Muuga Port, and the two businessmen now plan to resurrect the building in the Estonian capital Tallinn.
Speaking about the building, Sander Pullerits, project manager of the reconstruction programme, told the Baltic Times: 'It's an architectural gem.'
'They didn't preserve the cheaper stone, but there is still a lot of the original interior. There are marble columns, arches, staircases, balustrades, several fireplaces, wall panelling, and even old telephone booths.
'Unfortunately some of it was destroyed in the bombing, including the beautiful glass dome which was one of the most important parts. We will restore the rest as the building is constructed,' added Pullerits.
The complete rebuild is expected to take up to two years. New uses for the building have not yet been determined, but may include offices and also a space for the national maritime museum.