Even with all the surprises that have characterized Clint Eastwood’s twilight film years, with their crepuscular tales of good and evil, the tenderness of the love story in “J. Edgar” comes as a shock. Anchored by a forceful, vulnerable Leonardo DiCaprio, who lays bare J. Edgar Hoover’s humanity, despite the odds and an impasto of old-coot movie makeup, this latest jolt from Mr. Eastwood is a look back at a man divided and of the ties that bind private bodies with public politics and policies. With sympathy — for the individual, not his deeds — it portrays a 20th-century titan who, with secrets and bullets, a will to power and the self-promotional skills of a true star, built a citadel of information in which he burrowed deep.

To find the man hiding in plain sight, Mr. Eastwood, working from a smart script by Dustin Lance Black (“Milk”), takes a dynamic approach to history (even as it speaks to contemporary times), primarily by toggling between Hoover’s early and later years, his personal and public lives, while the director of the Federal Bureau of Investigation. The film opens in the early 1960s with a shot of the Justice Department building, the original home of the bureau, establishing the location, as well as the idea that this is also the story of an institution. As Hoover croaks in the voice-over (“Communism is not a political party — it is a disease”), the scene shifts inside, where the camera scans the death mask he kept of John Dillinger, former Public Enemy No. 1, and then stops on Hoover’s pale face: a sagging facade....