rs, 20 bytes

#
+#(.*)(.)/\2#\1
#/

Technically, this doesn't count (rs was created earlier this year), but I didn't see any other regex-based answers, and I thought this was neat.

Live demo.

Explanation:

#

Insert a pound character at the beginning of the string. This is used as a marker.

+#(.*)(.)/\2#\1

Continuously prepend the last character of the main string to the area before the marker until there are no characters left.

#/

Remove the marker.