Place the strawberries, sugar, and water in a saucepan set over medium heat. Simmer for about 10 minutes, stirring occasionally, until slightly thickened and juicy.
Set a fine mesh strainer over a bowl and pour the strawberry mixture through the strainer. Use the back of a spoon to press the strawberries against the strainer, extracting as much juice/syrup as possible. Chill the syrup.
Combine all ingredients in a pitcher and stir. Chill for several hours to allow the flavors to combine. Serve chilled over ice.