Krishnan took over from Lt Gen Shakti Gurung, an official statement said.
Gurung has been transferred to Integrated Headquarters of Ministry of Defence (Army) for his new assignment.
Krishnan, an alumnus of National Defence College, has held a wide range of command and staff appointments during his 36 years of service.
He is an expert in counter insurgency warfare and had earlier served in Operation Rakshak in Jammu and Kashmir, Operation Rhino in Assam and Operation Hifazat in Manipur.
Krishnan also had a tenure in Operation Meghdoot on the Siachen Glacier.
His earlier command appointments include command of an infantry battalion in the Kashmir Valley, an infantry brigade on the Western front and a division sized force in counter insurgency operations area in the North East.