Put water, both kinds of sugar, and cinnamon sticks in a medium-size saucepan and bring mixture to a boil.
Once boiling, lower heat and let mixture simmer for about 10 minutes, until syrup has thickened (note that it will continue to thicken as it cools).
Remove from heat and stir in vanilla extract. Strain cinnamon sticks out of syrup and pour into a heat-proof bowl or mason jar. Place bowl or jar in fridge to cool completely before using.