If The One Ring's report is correct, production will be based at the studio complex located in Leith, just outside Edinburgh, in a new studio complex.
The One Ring is a Tolkien fansite which attracted widespread attention when it gained exclusive access to the filming of Jackson's original trilogy in 1999-2003, regularly breaking stories and featuring exclusive content. They don't seem to have the same access to Amazon, and recently claimed the series would focus on the adventures of young Aragorn. Instead, Amazon have confirmed (twice) that the series will be set in the Second Age of Middle-earth. However, local press have backed up the report by saying that Amazon is leasing the required studio space, which is difficult to keep secret.
If true, it sounds like Season 1 of the show will be shot between August 2019 and spring 2020, to debut on Amazon Prime probably in early 2021.