Cousins died in Sydney (Australia) on New Year’s Eve 2017 after a seaplane plunged into a river 30 miles (50km) north of the city, along with the pilot, his fiancée, her daughter and his two sons.
The newspaper reported that his will specified that the money should go to the charity because his two sons died with him.
A spokesman for the charity said: “We are extremely grateful for this bequest of which we have only recently been notified.
“We are working with the family and our board of trustees to identify how the money would be used.”
In its annual report for 2016-17, Oxfam received £19.8m in gifts left through wills, so the amount left to it by Cousins will almost double on last years' donations.
It comes as Oxfam faced financial difficulty in the wake of allegations that its staff hired prostitutes while working in Haiti after the 2010 earthquake, resulting in four employees fired for gross misconduct and three others, including the country director, Roland Van Hauwermeiren, were allowed to leave the charity.
After the allegations emerged, thousands of people stopped making regular donations and in June Oxfam said it would be making £16m in cuts because of reduced funding.