Army Generals are NOT elected. They are appointed, with the consent of the Senate, by the President, as Commander-In-Chief of the US Armed Forces. Lincoln had appointed General George Mcclellan as Commander of the Union Army, but replaced him when little success was achieved in fighting the Civil War.
Abraham Lincoln appointed Ulysses S. Grant to lead the Union Army during the American Civil War. Grant, who had previously demonstrated effective military leadership in various battles, was named General-in-Chief of the Union Army in March 1864. His strategic approach and relentless pursuit of Confederate forces played a crucial role in the Union's eventual victory.
Following the Union defeat at Fredericksburg in December 1862, President Lincoln replaced General Ambrose Burnside with General Joseph Hooker. Hooker was appointed to lead the Army of the Potomac, and he was tasked with revitalizing the Union forces and improving their strategic effectiveness in the ongoing Civil War. Lincoln hoped that Hooker's leadership would reinvigorate the army after the significant losses at Fredericksburg.
Robert E. Lee
Robert E. Lee was offered command of the Union forces at the start of the Civil War. However, he declined the position, choosing instead to side with his home state of Virginia when it seceded from the Union. Lee's decision to lead the Confederate Army ultimately made him a prominent military figure in the war.
Lincoln couldn't declare war, because that would mean recognising the Confederacy as a sovereign nation. But he responded to the firing on Fort Sumter by calling for new volunteer-troops - which was the equivalent. Nothing much happened for a few weeks. A small Union victory in Western Virginia was blown up by the press into a major triumph, and Congress started to demand a big march on Richmond. In July, the luckless General McDowell had to lead the advance into Virginia, knowing that his army was not ready for operations. The Confederates won the ensuing battle, but were not able to pursue and destroy the Union army. It would be another seven months before anything significant happened, and that would be in the West.
George Brinton McClellan.
After the liberation of the Mississippi, Grant was ordered East, to rescue the Army of the Cumberland from starvation at Chattanooga.
General Robert E. Lee
The Union Army had several leaders. Some of them were George McClellan, William Tecumseh Sherman, and Ulysses S. Grant. Abraham Lincoln was President during the Civil War.
First of all, Vicksburg is not a state, it's a city. Second, Robert E. Lee was approached by Lincoln to command the Union army because of his views against slavery. Lee declined saying that if his home state of Virginia seceeds from the Union, he will go with it.
The vicksburg Campaign convinced Lincoln that Grant was the right man to lead the whole Union Army.
Shorter and less deadly.
US President Lincoln appointed Nathaniel P. Banks, the governor of Massachusetts to the position of general. He was to raise an army from his state and be available to lead a sea-land expedition to retake Texas for the Union.
After McDowell's failure at the First Battle of Bull Run, George McClellan was ordered to lead he Union army in the east. This was order was given by Lincoln.
Abraham Lincoln
Hooker, Meade, and Grant.
If the question pertains to the US Army of the Potomac, the last general to lead all the Union armed forces was Ulysses S. Grant. He was appointed by Lincoln and only reported to Lincoln. Whom ever might be leading any part of the Army of the Potomac, they reported to Grant. Grant was the last of a long line of generals to be appointed to lead all the Union forces.