Self Hosted WordPress can’t import directly Tumblr Posts as it does with LiveJournal or Blogger.

However, Importing and Displaying Tumblr posts on WordPress can be done indirectely through different methods, lets check each one of them.

1. Tumblr to WordPress Export Tool

This page has a Tumblr post export tool that transforms the posts into an xml file ready to be imported into WordPress.  Be sure to read each of the options available and also to choose the option Export For self-hosted WordPress.  Now in your wordpress go to Tools >>> Import >>> choose WordPress . You might be asked a few question to get the content organized, but that’s pretty much it.

2.  Reading and Saving your Tumblr XML, Then Importing to WordPress

LaurenTK blog gives us a really detailed explanation on how to do this, It’s not a one step solution but it works anyways.

3.  Using the Tumblr API to create a plugin for WordPress

This is only for developers, and Im still to find out a plugin that allows the import of Tumblr into WordPress displaying the content properly.

4. phptumblr, API wrapper

phptumblr.  Again, this is only for web developers with some knowledge of php and how to implement it in wordpress, it makes use of the Tumblr api to import Tumblr posts with the hmlt format you want.

5. Using WordPress Plugins, Feedwordpress and inline RSS

Feedwordpress inlinerss.  This wordpress plugins allows you to syndicate content from feeds (rss, atom).  This means it also works with Tumblr.  This is the right option for people with no knowledge of programming.