The junior Deora, 34, will be minister of state for communications and information technology.
The senior Deora had earlier this month offered to resign to Congress president Sonia Gandhi following media reports about his involvment in alleged irregularities during his tenure as petroleum minister from January 2006 to January 2011.
He had however cited "personal reasons" for stepping down and denied he had "anything more", including his son's inclusion in the council of ministers.
The son, one of the youngest members of the 15th Lok Sabha, was elected from the Mumbai South constituency for the second time in the 2009 elections.