There were a few victorious Union generals in the Civil War but most people would name Ulysses S. Grant first. It is true that Grant was the leader of all the armies of the north but Phillip Sheridan and William T. Sherman were just as important if not more so. Since Grant was in charge most of the praise goes to him, but he could not have done it without all the hard work of Sheridan and Sherman!
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During the Civil War and even long after, the two most well-known (and, in various senses, popular) generals were Ulysses S. Grant of the North and Robert E. Lee of the South. These two generals were admired for their military leadership skills and achievements as well as for virtues particular to each: the persistence and resolve of Grant, the grace, kindness, and commitment to honor of Lee.
At the start of the Civil War, Winfield Scott was the Commanding General of the Union Army.
As the Union forces effectively ended the "rebellion" of the Southern States, it's clear that the Union was the victor. This answer is strictly meant to answer the military outcome of the war. In a broad general sense, the Civil War, was a disaster in American history. The consequences were terrible for each side. In that sense, there was no victory, only a "result" in which the entire nation suffered.
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Ulyses C. Grant for the Union and General Lee for the Confederacy
The general in chief of all Union armies at the end of the war was Ulysses S. Grant.