The terrorists belonging to various banned militants groups were convicted by special military courts set up after the Peshawar school attack of December 16, 2014 to try militants.
The four were "hardcore terrorists" who were involved "heinous offences related to terrorism, including killing of civilians, officials of Law Enforcement Agencies and Airport Security Force," the army said.
They planned and executed attacks on Jinnah International Airport Karachi, CID building Karachi, ISI Office in Sukkur and convoy of law enforcement agencies, the army said.
Army said fire-arms and explosives were also recovered from their possession.
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The convicts were identified as Attaur Rehman, Muhammad Sabir, Farooq Bhatti and Gul Zareen.
It is unknown if they were tried when awarded initial sentence as the military courts operate in secrecy due to threat of backlash by the terrorists.
General Bajwa, 57, took over the command of the army on Tuesday at a ceremony in Rawalpindi from General Raheel Sharif who retired on November 29.