It seems that Manga Entertainment is releasing Professor Layton and the Eternal Diva on DVD and Blu-Ray in the UK on October 4th. The film will be released in a few ways. A disc-only DVD, and a disc only Blu-Ray editions. There will also be a phantasmagorical collector’s edition which comes in both a DVD, and Blu-Ray formats, and features gorgeous packaging and even includes an art book full of storyboards.
If you’re in the US, it’s easy to order from Amazon UK. I’m pretty sure region free DVD players exist as well for cheap.