How to 'linkify' plain text URLs (locally) on the Mac?

I'm copying a slab of plain text that contains URLs into an RTF file in TextEdit, which I am hoping to automatically, (as there are a lot of them in the text), 'linkify' into rich text hyperlinks - make them clickable, and underlined in blue or as per the default appearance.

In WordPad on Windows, if you paste plain text, WordPad will automatically linkify any links, but TextEdit, Word 2011, and Pages on the Mac all will not.

I've also tried to export the text to PDF in TextEdit, Word 11 and Pages and fiddled around with Tools in Acrobat Pro itself - all to no avail.

An AppleScript would be fun, but (even if hooked into FastScripts), still not as quick or elegant as Windows' WordPad's instant and automatic linkification of URLs upon insertion into a document.

Is there something this elegant in OS X?

To convert multiple plain text URLs to hyperlinks in a rich text file in TextEdit, you must apply an action.

After pasting the text, go to Edit > Substitutions > Show Substitutions, making sure 'Smart Links' is ticked, and either select the text and use 'Replace in Selection' or use 'Replace All' to apply to whole document itself:

EXAMPLE:

I pasted same text twice for demonstration.

After pasting I selected the second paragraph (only for demonstration) and used the Smart Links - Replace in Selection: