McChrystal, who replaces Gen. David McKiernan, is charged with trying to turn around the increasingly more violent situation in Afghanistan, as Gen. David Petraeus did in Iraq, The New York Times reported.
McChrystal has broad experience Special Operations, which have been criticized roundly by Afghan leaders for increasing civilian casualties caused by airstrikes.
"The measure of effectiveness," Gen. McChrystal has said, isn't by the number of enemy killed, but by "the number of Afghans shielded from violence."
Defense Secretary Robert Gates announced McChrystal's appointment a month ago, and it was confirmed last week by the U.S. Senate.
NATO has about 65,000 troops from 42 countries in Afghanistan, including about 56,000 U.S. troops.