Amazon have not officially confirmed the news as yet, but multiple crew members have marked the completion of shooting with social media posts.
They can't rest easy for too long, however, as production is rolling straight into Season 2. The cast and crew are still in Prague (with Lan reportedly stealing Moiraine's Golden Globe Award a few days back), and casting and pre-production on the second year is already in full swing. Whether actual shooting will continue immediately into the second season or there'll be a short break is unclear.
Shooting for the bulk of the first season was completed back in November 2020, with just a few last scenes being needed to complete the season. VFX, music scoring and post-production have continued through the pandemic, meaning that it hopefully will not take long to integrate the newly-completed scenes into the finished episodes. This makes an autumn air date on Amazon Prime quite possible.