The contest, which required a runoff vote to secure a 52-percent majority for AKK as she is known, is expected to increase the likelihood that Merkel will be able to see out her fourth term until 2021.
"We must have the courage to stay the course against the Zeitgeist," she said.
AKK beat corporate lawyer Friedrich Merz, 63, who had quit politics in 2009 after losing a power struggle to Merkel and long nursed a grudge against the more centrist chancellor.
The third candidate -- vocal Merkel critic and current health minister Jens Spahn -- lost in the first round.
Merkel, 64, had earlier mounted a staunch defence of her moderate course since becoming chancellor in 2005.
Accepting a lengthy standing ovation from delegates, many tearful and holding "Thanks, boss" placards aloft, a visibly moved Merkel said the party had won four national elections under her by holding fast to its principles.
"In difficult times we shouldn't forget our Christian and democratic stance," she said.
Pointing to the rise of populism worldwide and what she called a breakdown of shared Western values, Merkel acknowledged the order she had championed was at risk.
"Whether it's the rejection of multilateralism, the return to nationalism, the reduction of international cooperation to deal-making or threatened trade wars... hybrid warfare, destablisation of societies with fake news or the future of our EU -- we Christian Democrats must show in the face of all these challenges what we've got," she said.
Her modest style, even temper and largely middle-of-the-road policies mirror Merkel's, while both women are respected for the flash of steel they have shown at decisive moments.
While she has called for tougher policies on refugees who commit crimes, AKK firmly backed Merkel's fateful 2015 decision to welcome more than one million asylum-seekers from crisis zones such as Syria and Iraq.
She won a tough re-election battle in her native Saarland state on the French border in 2017, briefly halting a series of poll debacles for the CDU as it was racked by infighting over the refugee influx.
During her campaign to succeed Merkel as party leader, she repeatedly noted that she was able to blunt an onslaught by the anti-immigrant Alternative for Germany (AfD) party as it picked up seats in state after state.
AfD parliamentary group leader Alice Weidel relished the prospect of AKK as an opponent.
"With her, the CDU's leftist course will continue and so the last conservative Christian Democrats have lost their fight and no longer have a political home in the party," she tweeted.
Merkel has moved the CDU steadily toward the political centre during her long tenure. More generous family leave, an exit from nuclear power and an end to military conscription are among her signature policies.
The CDU has bled support to the right in the form of the AfD, as well as to the resurgent Greens.
Meanwhile Germany's oldest party, the Social Democrats (SPD) -- junior partners in Merkel's "grand coalition" -- are mired in an even deeper crisis.
The party has long languished in Merkel's shadow and could well decide to jump ship before 2021 to seek to avert further vote debacles -- a move that would almost certainly trigger new elections.
"You have big shoes to fill -- good luck," she tweeted. (AFP) SCY
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