Normally you can do a spring cleaning. Use a mildewcide. Most home centers have them where the deck cleaning prooducts are located. Give it a good scrubbing with a somewhat stiff bristle brush, then rinse.
If the wood was teak or mahogany, and silvered due to UV exposure, your cleaning will remove the silvering and the furniture will require another year to weather.
Make sure the cleaner is allowed to be used on your wood. Some cleaners can damage softwoods.