what was the result of the battle of vicksburg
The Confederates surrendered.
Siege of Vicksburg
After holding out for more than forty days, with their supplies nearly gone, the garrison surrendered on July 4. The successful ending of the Vicksburg campaign significantly degraded the ability of the Confederacy to maintain its war effort. This action, combined with the surrender of the down-river Port Hudson to Maj. Gen. Nathaniel P. Banks on July 9, yielded command of the Mississippi River to the Union forces, who would hold it for the rest of the conflict.

The Confederate surrender on July 4, 1863, is sometimes considered, 
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Siege of Vicksburg [SEP] Introduction
After holding out for more than forty days, with their supplies nearly gone, the garrison surrendered on July 4. The successful ending of the Vicksburg campaign significantly degraded the ability of the Confederacy to maintain its war effort. This action, combined with the surrender of the down-river Port Hudson to Maj. Gen. Nathaniel P. Banks on July 9, yielded command of the Mississippi River to the Union forces, who would hold it for the rest of the conflict. The Confederate surrender on July 4, 1863, is sometimes considered, when combined with Gen. Robert E. Lee's defeat at Gettysburg by Maj.