I know there are a few others out there who are going to be interested in transferring saves between old systems and new ones, so here's the quick and dirty on what you'll need to do. Keep in mind that saves will only transfer between prior gen consoles to their new successors. You can't transfer from an Xbox to a PS4, for example.

Turn on your old console, load the game, and install its latest update. The cross save update hits sometime this week, so if the following option isn't there, just wait a few days.

From the game's main menu, choose Cross Save or Cloud Save.

From the Handsome ajack Collection, download your save from the game's main menu.

All information is courtesy of Gamespot. Note that only one save can be transferred at a time, but by repeating this process to completion with each save, you can transfer all of them.

It should be noted that Golden Keys and items in your Shared Stash will NOT be transferred. So be sure to remove the items from your Stash and put them in a character's inventory or bank, then spend your Golden Keys.

Thanks for the info

So I really need to export/import each character one at a time? That's quite silly.

@bigdaddy81: Oh good tip. I hadn't read that part.

I was happy to find out on the PS side of things, you don't need a paid PS+ account for the transfer. Just the console account you use needs to tied to a free PS account, even if the characters were originally created before the console account was linked to a PS account.

Also, I was able to upload all my characters in one shot, then download all my character in one shot, not sure about this one at a time thing, maybe that's an XBox thing or just the instructions being overly cautious. (well technically I could upload all the characters in one game under one account in one shot).