The convicts were sentenced to death by a military court and are the first to be hanged in relation to the attack.
Taliban militants stormed the army run public school in the capital city of Khyber- Paktunkhwa province, Peshawar, on December 16, 2014.
The hangings came just two weeks ahead of the anniversary of the attack, which shocked the nation.
The massacre prompted a crackdown on Islamist militants, the establishment of military courts to try terror suspects and the resumption of capital punishment after a six-year moratorium.
These executions are timed to coincide with the first anniversary of the Peshawar school massacre. The trials were held in a military court and the proceedings were shrouded in secrecy.
A recent military statement claimed the convicts were linked to the little known Toheedwal Jihad group of the Pakistani Taliban. It said they admitted to involvement in previous attacks on military targets, including the 2012 assault on the air force base in Peshawar. However, it did not specify how they were linked to the school attack.
After the school attack, the government decided to set up military courts to try civilians involved in terrorism. The move was opposed by human rights groups who argued it would lead to miscarriages of justice and summary executions.
Earlier this week, Army Chief Gen. Raheel Sharif, signed black warrants for the four militants who were named as Maulvi Abdus Salam, Hazrat Ali, Mujeebur Rehman and Sabeel.
Security officials said the four men were executed early on Wednesday at a jail in the north-western city of Kohat.