Put the metal end of the hoe into a bench vice. Tighten the vice enough to securely hold the tool in place. Remove the screws that are holding the broken handle in the tool's metal sleeve.
Pull out the old handle. If the handle is wedged in too tightly or has broken below the end of the metal sleeve, insert a few wood screws into the broken end. Grip the heads of the screws with a pair of pliers or locking pliers such as Vice-Grips and pull out the old handle.
Clean out the metal sleeve completely before installing the new handle. Use a coat hanger or a file to remove any remaining handle pieces.
Apply a coat of varnish to the new handle if it does not already have a protective coating. Pay special attention to the portion that gets inserted into the metal sleeve. This helps seal the wood against moisture, which can eventually weaken the handle. Allow the handle to dry.
Insert the handle into the metal sleeve and secure it with screws. Start the screws with a regular screwdriver, then use a power screwdriver to tighten them up. Avoid overtightening, as this could cause the wood to split. Screw them in deep enough so that they do not protrude.
Put the metal end of the hoe into a bench vise. Tighten the vise enough to securely hold the tool in place while removing the rivets. Removing the rivets is not easy; it may take several attempts.
Drill out the heads of the rivets as the first attempt at removing them. If this does not work, try sawing off the rivet heads with a hacksaw. You can also try filing the heads off with a metal file. If all else fails, use a hammer and punch to push the rivets into the wooden handle.
Complete the process by following the instructions in Step 2 through Step 5 for handles with screws. You'll use screws, not rivets.