'Hero of Russia'
Yevkurov is a 45-year-old Ingush who led operations against Chechen fighters during the fighting there.
He has been decorated a "Hero of Russia", the country's highest honorary title.
Yevkurov also commanded Russian troops in 1999 to take control of Pristina airport in Kosovo before advancing Nato troops could reach it - an operation that angered the United States but was seen at home as a daring coup.
"This is a tough guy, very tough," said Alexei Malashenko, a security analyst with the Carnegie Moscow Center think-tank.
"He is an energetic person, young, and, since he will have complete 'carte blanche' from Moscow, I think he will restore order."
Ingushetia's regional parliament voted to approve Yevkurov as its new leader on Friday, an official in the parliament's press service said.
Russian regional leaders are nominated by the president and confirmed by local legislatures.
Yevkurov flew to the region on Friday and was greeted at Magas airport by members of the local opposition performing traditional dances.
Analysts say the uprising in Ingushetia is driven by a mixture of anger at poverty and corruption, reprisals against security forces, and Muslim groups who want to throw off Moscow's rule.
Human-rights groups estimate that 93 people had been killed there up to the end of August.
Zyazikov's critics accused him of aggravating the uprising through economic mismanagement and heavy-handed security operations that failed to discriminate between civilians and fighters.
Protests took place in September when Magomed Yevloyev, the unofficial leader of the opposition, was shot dead in police custody.
Investigators said a police officer had accidentally fired his gun at Yevloyev's head.
Zyazikov used to serve in the FSB state security service, the main successor to the Soviet Union's KGB secret police.
Groups of men danced in the streets of Ingushetia's main city, Nazran, as they celebrated his departure.