How do I migrate to Tumblr without breaking existing post URLs?

I have a blog. I don't like running it myself. People link to specific posts, and they're indexed by search engines. I want to keep those post URLs and move them to Tumblr (it's on a subdomain, which I'd point to Tumblr).

I couldn't find an answer on GetSat, yet it seems like a problem that any existing blog would have, so I'm hopeful.

What's the best way to solve it with Tumblr? Best for me: let me pick URL paths for my existing posts.