Why did the siege of Vicksburg succeed when attacks in Vicksburg had failed?
Federal assaults on Vicksburg failed in more than one attempt to capture this important Confederate stronghold on the Mississippi River. For example the first attempt to force Vicksburg to surrender by Admiral Farragut was a dismal failure. The key was the excellent defensive position of this fortress city. It was high on a mountain-like bluff. It had ample cannon support to hamper assaults from the Mississippi River, and to a large extent it was protected by swampy land, making military assaults very difficult. As an aside, the final capitulation of the fortress-city stronghold put to lie the contention by Union General Halleck that the Confederacy held a distinct advantage because of its interior position. The position, however, did display how difficult it was at various points in time of the war, for even overwhelming Union troop numbers to succeed at will in its Western theater adventures. The use of the term "overwhelming" is not exaggerated. For example, it took Grant's forces of 23,000 troops to over run a Confederate defending force of 6,000 troops in one early part of the upcoming siege.
General Grant's strategy to encircle Vicksburg and cut off all resupply meant that all of the townspeople and many thousands of soldiers would have to live on the small amount of food available. The southern attempts to break the blockade failed and the food ran out.
The purpose of capturing Vicksburg was to shut down a huge supply city the Confederacy relied on. Also, Vicksburg being on the Mississippi River, needed to fall allowing the Union full access to this key river. The problem was that Grant failed in attempts to capture Vicksburg early on in the war. His strategy of a river attack failed. Only later in the War did the siege of Vicksburg succeed.
The first assault on Vicksburg began on May 19, 1863. The assault failed so Ulysses S. Grant launched another assault on May 22; this time with his full force. The second assault was also a failure. After two failed attacks Grant lay siege to the city on May 25, 1863. After six painful weeks of fighting and starvation Lieutenant General John C. Pemberton surrendered the fortress of Vicksburg on July 4, 1863.
Better said was the "battles to capture Vicksburg". At least three Union attempts failed to actually capture the city fortress of Vicksburg. Only via a siege was the city captured. And, yes this at last gave the Union full control of the Mississippi River. This was now the western base from which to launch assaults on either side of the river.
Answer The Battle of Champion's Hill, just east of Vicksburg, was fought on 16 May 1863. This battle was fought out in the open and was a set-back for the Confederates. This forced them to return to the defenses of Vicksburg, which began the siege. The siege ended when General Pemberton surrendered Vicksburg on 3 July.