Can you move previous world data into a Minecraft Realm?

After multiple at home servers crashing, I'm trying to decide if purchasing a realm would be worth it.

My only question is if you can move pre existing worlds into a new realm? So say I purchase a realm for 13/month, could I upload the world we're using now onto it?

Any feedback would be greatly appreciated, thanks.

MrLemon is correct as of Minecraft 1.7.9. However, Minecraft 1.7.10 came out literally today, June 26; Searge tweeted that it was released between MrLemon's answer being posted and mine being posted. It includes the following changes for Realms:

World uploader – upload your local world to Realms (finally!)

Command blocks! (finally!)

Player activity monitor – when and for how long a player has been online (see who plays when you sleep!)

Access to more server settings (yey!)

Improvements in Realms UI (also yey!)

--Source (emphasis mine)

So yes, you can. Happy Realms-uploading day!