Analysis
Historical records of Mosaddegh's April 13, 1951 speech contain language similar to the quoted statement, confirming he expressed gratitude to God and the army and declared the nationalization of oil. However, while the law transferred ownership to the Iranian government, British interests continued to dispute the move and Iran lacked full operational control of production and export until later negotiations, making the claim about "our oil is now in our own hands" only partially accurate.
Background
In March 1951, Mohammad Mosaddegh's government passed the Oil Nationalization Act, ending the Anglo-Iranian Oil Company's monopoly. The move was popular domestically but provoked a diplomatic and economic crisis with Britain, leading to a prolonged standoff and eventually the 1953 coup that overthrew Mosaddegh. The nationalization was a symbolic assertion of sovereignty even though practical control lagged.
Verdict summary
Mosaddegh did make a public address after the 1951 oil nationalization praising God, the army, and claiming oil was now Iranian, but the practical control over oil remained contested.