Reconstruction ended as a result of a compromise made to elect Republican Rutherford B. Hayes to the presidency over the Democrat Samuel J. Tilden. Tilden had won the popular vote and a plurality of electoral votes but some remaining electoral votes were in dispute. A commission was set up made of 5 Senators. 5 Representatives and 5 Supreme Court Justices -- 8 Rs, 7 Ds -- to adjudicate the matter. A compromise was reached in which the disputed electoral votes were given to Hayes in return for the end of Reconstruction.
http://www.pbs.org/wnet/jimcrow/stories_events_election.html
Better not to mention this.
For all practical purposes, Reconstruction ended when the Democrats won control of the House of Representatives in 1874. They then vowed to withhold appropriations from the Army unless remaining occupation forces were withdrawn from the South. By the time of the Compromise of 1877, Democrats were back in control of most of the former Confederacy, except in Louisiana, Florida, and South Carolina, where a few companies of soldiers kept the elected Republican Governors in office. Hayes did agree to withdraw those soldiers -- fewer than 1,000 total -- from those state capitals and allow Democrats to evict the Governors. That's all the Hayes concession to Tilden amounted to. Of course, had Tilden won, it all would have happened anyway.