With all of the shock absorption that the handle of an axe takes, it will likely get damaged or break at some point. Here are the steps you need to take to replace an axe handle:

Remove the handle from the head
Before you put the new handle in, you will obviously need to take the old one out. Put the axe head in a vice with the majority of the handle facing down. Take a hammer and chisel and use them to drive down the visible handle wood in the middle of the head.

Select a new handle
The next step once you get the handle out of the head is selecting a new handle. Bring the old head with you to the hardware store and have an employee in the know help you select one. Typically axe heads are hickory and should come with some wood shims. The handle should also have a slit at the end where a shim can go.

Installing the handle
Put the axe head over the handle and use a wooden mallet to drive the head onto the handle. When you do this, the handle should be fairly snug and fit pretty well onto the head. Next take the shim you have and drive it into the slit in the middle of the handle. This will expand the wood out to the handle and make it so the handle is permanent. Make sure that the shim doesn’t have any part sticking out of the top.

Test run
At this point your axe should be ready for a test run. Take it outside and take a few cautious swings with it. If the head still feels a little loose you can drive another shim into it.