Final answer:
During the American Civil War, General David Farragut was the Union commander responsible for seizing New Orleans, Baton Rouge, and Natchez, as part of the Union's strategy to control the Mississippi River.
Step-by-step explanation:
The Union commander who seized New Orleans, Baton Rouge, and Natchez is General David Farragut. This operation was a part of the broader strategy to gain control of the Mississippi River during the American Civil War. While General Ulysses S. Grant was significant in winning battles in the western theaters, such as at Shiloh, and later leading the Union to overall victory, it was General Farragut who captured the key southern ports of New Orleans, Baton Rouge, and Natchez, thereby aiding the Union's efforts to divide the Confederacy by controlling the Mississippi. Farragut commanded the Union fleet during the Battle of New Orleans in 1862, successfully capturing the city and securing control of the Mississippi River for the Union.