So, you're migrating your blog. Good for you! If you're running your tumblr blog on your own domain (yourdomain.com rather than me.tumblr.com, for example), then you can set up redirects from the old URLs that people are still linking to, to the imported post on your new WordPress blog.
Basically, where you have a Tumblr post URL that looks like this: http://example.com/post/12345678/this-is-a-post, the only part that matters is http://example.com/post/12345678/. That number is the ID. Everything after that gets ignored when Tumblr loads the post.
When you export your post, you're encouraged to include that post ID in the new permalink slugs, since that way you can redirect from one to the other.
If you take your current Tumblr custom domain, and host it yourself, you can set up a simple .htaccess redirect for people linking to your old posts:
RewriteEngine On RewriteRule ^/?posts/([0-9]+).*$ http://wordpress.example.com/blog/$1