In an ultimate sense, the leader of the Manhattan Project was President Franklin D. Roosevelt since the project was an Army project and he was commander in chief of the armed forces. However, that is probably not the answer you are looking for. The person who is most closely connected with the Manhattan Project was General Leslie R. Groves. General Groves was chosen to head the project and was in charge of or involved in almost every aspect of the project, from the selection of sites for production plants to the selection of targets on which the bombs would be dropped.
Roosevelt authorized the Manhattan Project.
Dr. Robert Oppenheimer is often referred to as the "Father of the Atomic Bomb." A team of United State's physicist's were called upon by the Franklin D. Roosevelt administration to to beat Nazi Germany in the race towards a nuclear weapon during World War II. Oppenheimer recruited some of the best scientists the United States had to offer in developing the nuclear bomb at a research facility located in Las Alamos New Mexico. This project was referred to the Manhattan project.
After about three years of developing the bombs, the group successfully tested the first nuclear bomb in the dessert of New Mexico in July of 1945.
General Groves, who at the time of his selection to head the Manhattan Project was a colonel, wrote a totally cool book ( Now It Can Be Told: The Story Of The Manhattan Project by Leslie R. Groves) about the making of the atomic bomb.
I don't remember that President Roosevelt had anything to do with the making the bomb, except he must have had to select Groves, who had recently finished building the Pentagon. Like the previous poster said, Groves had a hand in all of it. He selected Tibits to train the flight crews in Utah. He selected Oppenheimer to lead the scientists to research and design the bomb in New Mexico. He selected DuPont for building facilities for making parts of the bomb. He even selected the targets.
One story, which I remember, might indicate how the White House had some involvement in building the bomb. Kyoto was on the original list of targets for the first bomb. I don't remember for sure, but I believe Roosevelt had to approve the list. The list, which Groves submitted to be approved, did not include Kyoto because someone in the chain of command was a scholar of Japanese culture, and that person knew how important Kyoto was to Japan. He thought that the destruction of Kyoto would so enrage the Japanese that they would never surrender.
I'm doing this from memory. Maybe one should double check what I have said.