Kruger, currently president of ExxonMobil Production Co, will take over at Canada's second-biggest integrated oil company on March 1.
Kruger, currently president of ExxonMobil Production Co, started his career with Exxon in 1981.
March has been appointed senior vice-president of global operations for ExxonMobil Chemical.
Imperial Oil, in which Exxon holds 69.60 percent, is best known for its dominant position in the Alberta oil sands.
The company reported a higher fourth-quarter profit earlier this month but said costs of its recently completed Kearl oil sands project in northern Alberta have risen by C$2 billion to C$12.9 billion ($12.7 billion).
Shares of the company, which has a market value of C$36.29 billion, closed at C$42.82 on the Toronto Stock Exchange on Wednesday.
($1 = 1.0148 Canadian dollars)
(Reporting by Bhaswati Mukhopadhyay in Bangalore; Editing by Sriraj Kalluvila)