All other answers suggest drag handles, but I suggest against that.
The problem with drag handles is that:
- you ask the user to move a block from one position to a specific area. If he misses the area, errors can easily occur.
- if the block you're moving is too high, the travel distance can become cumbersome.
- it can be hard to implement
- drag handles suggest that the item can be moved anywhere, but in this case, there's only one target
Drag handles work well with a list of N items, where each of these item take up a small amount of space, and where each item could be moved anywhere within the list.
Switch, not drag
Here, you just want to switch positions, between 2 items. There is only 1 start position, and 1 target position. Just use a toggle button.
For example, Google Translate uses a double-arrow button to toggle between the source language and the destination language:
Keep it simple
Don't give your users the illusion that can they can move items around anywhere with drag handles. Just have a single button that performs the single action of switching positions.