Cook beets in water to cover in a large Dutch oven over medium-high heat 30 to 35 minutes or until tender. Drain and peel. (If beets are too large for jars, cut into pieces.)
Bring 3 cups water and next 6 ingredients to a boil in a large heavy saucepan. Cover, reduce heat, and simmer, stirring occasionally, 10 minutes.
Pack hot beets loosely into jars, filling to 1/2 inch from top. Cover beets with hot syrup. Remove air bubbles; wipe jar rims. Cover at once with metal lids; screw on bands.
Process in boiling-water bath 30 minutes.