Lay a piece of newspaper on the floor. Flip over the ottoman and set the top on the newspaper. Trace around the top of the ottoman for a pattern.
Remove the ottoman and draw a second circle 1/2 inch outside of the first.
Measure the circumference of the ottoman base with a flexible measuring tape and multiply the number by two. Measure the height of the ottoman and add 1 inch to the number.
Cut a piece of fabric using the adjusted circumference and height measurements. Cut a circular piece of fabric using the pattern for the top of the ottoman.
Pin the circumference piece of fabric by matching the short ends with the right sides together. Sew the ends together with a 1/2-inch seam to make a tube. Finish the raw edges of the seam with a serger or zig-zag stitch.
Sew a row of gathering stitch about 3/4 inch from the top edge of the loop. Sew a second row about 1/4 inch from the top edge. Leave the thread ends about 4 inches long so you can grab them when gathering the edge.
Gather the top edge of the fabric loop by grabbing the starting thread from the top and bottom row. Pull the thread gently while sliding the fabric along the stitching. Gather the loop until it reaches the same measurement as the circumference.
Insert a pin next to the start and end thread of the gathering stitching, and then wrap the threads around it in a figure-eight pattern. This will prevent the gathering from coming undone.
Pin the gathered edge of the loop fabric to the round top fabric, matching the right sides together. Sew the pieces together with a 1/2-inch seam. Finish the raw edges with a zig-zag or serger stitch to prevent fraying.
Fold the bottom edge of the cover 1/4 inch to the wrong side, and then iron it to hold. Turn the edge under another 1/4 inch and iron. Sew the hem with a straight stitch to hold in place. You may want to pin the hem after turning the second edge to hold the fabric while you sew.