In the IAF, Air Marshal SBP Sinha took over as the Deputy Chief of the Air Staff and will look after modernisation of the force.
Lt Gen Krishnan, 58, would be in-charge of procurements in the Army, which is undergoing massive modernisation.
An alumnus of National Defence College, he has held a wide range of command and staff appointments during his 36 years of service.
An expert in counter-insurgency warfare, Krishnan had earlier served in Operation Rakshak in Jammu and Kashmir, Operation Rhino in Assam and Operation Hifazat in Manipur.
Air Marshal Sinha, 58, is a fighter pilot who has over 3,700 hours of flying experience having flown the Hunter, MiG-21, Mirage 2000 and Su-30MKI fighter aircraft.
He has held several important posts in the force and had headed the Airborne Warning and Control System (AWACS) Project Team in Israel.