Nicholson, 58, took over today from US Army General John F Campbell, who oversaw the end of the international combat mission in 2014 and an escalation in the Taliban's war against Kabul.
In a ceremony at the headquarters of the US-NATO Resolute Support mission in Kabul, Nicholson thanked NATO representatives for standing by the US after the September 11, 2001 attacks on "the homeland."
To the Taliban, he said: "I know you. You have brought only hardship and suffering to the Afghan people."