The report calls for the 27-nation bloc to increase industrial investment by hundreds of billions of euros a year and boost innovation to keep pace with the US and China.
Draghi, who was ECB president between 2011 and 2019, acknowledged that his proposals were "unprecedented".
The investment package would be a bigger boost than the Marshall Plan to rebuild Europe after World War II, he said, adding that it was justified by the existential challenge facing the bloc.
"The proposals in the report could help the ECB achieve better results in our monetary policy," Lagarde said.
"Raising productivity, deepening the capital markets union and more funding for innovation would be good news for the central bank. I very much hope that the responsible executives will actually take it to heart and see the way forward on these structural reforms," she added.
