After finishing his Bachelor's Degree with Honors at New Delhi University in India, Wakhweya returned home to become one of the first Ugandan district administrative officer on 5 September 1960 during the British colonial administration. Upon Ugandan independence from the United Kingdom, Wakhweya became the Assistant Secretary to the Treasury in the Milton Obote administration. This began a rapid career rise for Wakhweya in the Ugandan Treasury. He was promoted to Under-Secretary to the Treasury on 4 November 1965, Deputy Governor Designate of the Bank of Uganda in 1968, and finally appointed as the Minister of Treasury on 1 January 1969. Following the successful 1971 Ugandan coup d'état led by Idi Amin, Wakhweya was named Minister of Finance by Idi Amin for the newly formed administration, where Wakhweya was tasked with stabilizing the Economy of Uganda, which was rapidly deteriorating because of high state spending, a post-coup flight of foreign capital, and a lack of new investment from abroad.