As a result of the victory at Vicksburg, Union forces gained access to what river?

Along with the defeat of Robert E. Lee's army at Gettysburg, the Union forces that seized the heavily fortified city of Vicksburg , gained access (control) of the Mississippi River. This ultimately helped the Union to win the Civil War. Was this really that important in the end?

Control of the Mississippi River during the war was an economic and psychological factor for both the Union and the Confederacy. For many years, the river had served as a vital waterway for mid-western farmers shipping their goods to the eastern states by way of the Gulf of Mexico. The farmers, along with merchants and politicians, did not like the idea of the river being closed because of Confederate artillery looming along the banks where the “Father of Waters” flowed through the Confederacy.

For the Confederacy, control of the lower Mississippi River was extremely vital. In the state of Louisiana west of the river plus Texas and Arkansas, it formed the Transmississippi which held manpower and materiel that the rest of the southern military machine had to have to win the war. When Vicksburg fell to Union troops on July 4, 1863, the Confederacy lost a major key to defeating (if at all) the Union Army.