The above answer gives Lincoln far more credit than he deserves, and stretches his role in ending slavery to a fanciful extent. Lincoln did not begin the Civil War, let alone see it as a fight over slavery. In fact, he said many times that his purpose was to preserve the Union; he stated on occasion that if he could preserve the Union without ending slavery he would do so. As noted, the Emancipation Proclamation only freed slaves in those states "in rebellion," in which Lincoln's authority was not recognized. Also noteworthy is the fact that the Proclamation exempted certain areas in Virginia and Louisiana which were under Union Control, nor did it end slavery in the "border states" where it still existed. It is not coincidental that the Proclamation was issued shortly after the Battle of Antietam, where Robert E. Lee hoped to gain recognition of the Confederacy by European powers. The Proclamation, aside from giving the Union the moral high ground, also precluded the possibility of European intervention in the war; it did not end slavery, nor was that its purpose.
As far as pushing the war to a successful conclusion, Lincoln's general plan of amnesty of 1863 was far more lenient than that adopted by the Reconstruction Congress. Thus, it is a reach at best to credit Lincoln with ending slavery. It is more nearly correct to give that credit to the Congress which passed the Thirteenth Amendment.
Slavery was ended by the Thirteenth Amendment to the Constitution, which was passed by the Reconstruction Congress. Lincoln's intentions had he survived are problematic; however the circumstances one is left to consider are not convincing that Lincoln ended slavery.
Overall, this statement is accurate, though not in the way that many people think.
Many people argue that Lincoln freed the slaves through the Emancipation Proclamation. However, this is not a very accurate statement. The Emancipation Proclamation only freed those slaves over whom Lincoln had no control--those in areas that were "under rebellion" against the US. Lincoln did not free those slaves who were in areas still controlled by the US government.
However, Lincoln can be credited with freeing the slaves. The slaves were freed because the North fought and won the Civil War. Had it not been for Lincoln, it is quite possible that the war never would have been fought. It is also possible that the North would not have cared enough to see the war through to a successful end.
Since Lincoln was the driving force behind the war, and since the war freed the slaves, we can say Lincoln freed the slaves.