Certain political leaders, whatever their aspirations, become overwhelmed by events they once thought they could master. Think of Alexander Kerensky (cast aside by Russia’s October Revolution) or even Jimmy Carter (reduced to political impotence by stagflation and Iran). Other leaders, though, meet enormous challenges with a vision and a resolve that allow them to shape events and guide the course of history—think of Winston Churchill (defying Hitler), Margaret Thatcher (resurrecting Britain) or Helmut Kohl (reunifying Germany). To this second group belongs Alvaro Uribe Vélez, the president of Colombia from 2002 to 2010.

The country he inherited, upon his election, was a perfect hell. Various paramilitary groups and Marxist terrorist organizations, pre-eminent among them FARC (the Revolutionary Armed Forces of Colombia), controlled half of the country’s territory, often aided by Colombia’s left-wing neighbors, Venezuela and Ecuador. Every year, an average of 28,000 Colombians were killed and 3,000 kidnapped, usually to coerce a ransom. Drug traffickers generated $3 billion annually. Unemployment was close to 16%.

By the time Mr. Uribe left office, the homicide rate had halved and kidnappings had dropped to a 10th of what they once were. Most of the country had been cleared of terrorists, and 50,000 paramilitary troops had been demobilized. Under a more secure and business-friendly environment, foreign investment had doubled and exports tripled; economic growth was close to 7%. By lowering some taxes, introducing more flexibility in the labor market and promoting trade, Mr. Uribe helped trigger a boom that, by 2010, took the investment rate to 28% of gross domestic product from 13%.

Mr. Uribe’s feat was punctuated by daring moments, including the rescue of former presidential candidate Ingrid Betancourt, three American contractors and several hostages in 2008, when an intelligence mission broke the enemy’s code of communications and duped FARC into believing that the rescuers were humanitarian workers.

What is most interesting about “No Lost Causes,” Mr. Uribe’s engaging memoir, isn’t so much the narrative of his achievements but the insight he offers into his own character and the life experiences that created it. (Mr. Uribe has recently been nominated to be a director of News Corp., the owner of The Wall Street Journal.) The simplistic interpretation is that Mr. Uribe sought to avenge the murder of his father, killed by FARC in 1983. But his suffering wasn’t so strikingly dissimilar to that of tens of thousands of other Colombians whose lives had been altered by two decades of civil war (in the 1940s and 1950s) and decades of drug-related violence and Marxist terrorism. Just after his father’s murder Mr. Uribe served on a peace commission charged with exploring an end to the horror through dialogue.

In fact, Colombian democracy had tried Chamberlain-like appeasement several times; it was desperate for Churchillian mettle. The people found it in this man. “Learning how to control my emotions, and channel them for a constructive purpose,” Mr. Uribe writes, “took a lifetime of experience for me.” He spent his presidency visiting village after village to fight for the rebirth of civil society and imitating the meticulous discipline with which his father had overseen every task on the family’s farm.

Mr. Uribe tried to use self-control in dealing with his left-wing neighbors, Venezuela’s Hugo Chávez and Ecuador’s Rafael Correa. He made overtures and prevented escalations that might have led to all-out war. But he didn’t lose sight of the mission he had—to respond to their protection of FARC. So he crossed their borders when he had to, as in 2008, when Colombia bombed a FARC camp inside Ecuador, killing a top commander and seizing a treasure trove of information.

Mr. Uribe was in some sense a victim of his success—most notably with the demobilization of the paramilitaries, who, like FARC, were drug traffickers. Thanks to a deal, in 2005 he brought more than 35,000 of them into the open. Since it was difficult for these men to take jobs, some went back to crime. Some operated with impunity from prison, as in the past. (Eventually Mr. Uribe extradited the 14 key leaders to the United States.)

The process of extracting confessions was messy and revealed umbilical connections between paramilitaries and the establishment. More than 20 mayors, governors and members of Congress were convicted, as well as other politicians, including some former Uribe collaborators. Mr. Uribe’s critics blamed the widespread corruption on him, but he didn’t create the problem—he brought it to the surface and, yes, it looked very ugly. That said, Mr. Uribe reacted slowly to reports of illegal espionage and human-rights abuses in the struggle against FARC. “I believed that we could regain control,” he writes, “over 100 percent of Colombia’s territory while respecting human rights and extending the reach of democracy.” His sense of purpose led him to be less obsessively vigilant about the means than the end.

A few months after his inauguration in 2002, a FARC leader had said: “Uribe’s serious problem is that he has only three years left and FARC has all the time in the world.” Inevitably, a man with a messianic bent in the midst of a war found term limits cumbersome. The constitution was amended to allow him a second term, and he won re-election in 2006. In 2010, he let start a process that would have permitted yet another re-election. In the end, the constitutional court prevented it. Mr. Uribe admits it was “an error” not to halt the process himself.

A few weeks ago, Colombia’s current president, Juan Manuel Santos, announced that he will start formal peace negotiations with FARC. Nobody knows if they will end up like the many frustrated attempts since the 1980s. Whatever happens, the terrorists have never been closer to defeat, and Colombia is a country reborn—thanks to the efforts of Mr. Uribe and his brave countrymen.