Mr Macron is the first French president to be born after Algerian independence and hopes "to lay a foundation to rebuild and develop" a sometimes difficult relationship with the North African nation.
Algerian President Abdelmadjid Tebboune welcomed what he called the "encouraging results" of the visit, speaking alongside Mr Macron on Thursday evening.
Hailing a "positive dynamic" in their relationship, Mr Tebboune said there were "promising prospects for improving the special partnership that binds us".
Mr Macron landed earlier at Algiers' main airport where he was warmly greeted by the president and a military band that played both national anthems.
Later, the French leader visited a monument to those who gave their lives in Algeria's war for independence, laying a wreath and observing a minute of silence.
Mr Macron announced on Thursday evening that the two countries would set up a joint commission of historians to study archives on France's 130 years of colonial rule in Algeria, including the devastating eight-year war that led to independence in 1962.
"We have a common [but] complex and painful past," he said, explaining that the researchers would have full access to the archives.
Algeria celebrates 60 years of independence from France - in pictures
They had been particularly stormy since last year when Mr Macron questioned Algeria's existence as a nation before the French occupation, and accused the government of fomenting "hatred towards France".
Mr Tebboune withdrew his country's ambassador in response and banned French military aircraft from its airspace.
But Mr Macron's office said he "regretted" the misunderstandings caused by his comments, and his aides believe both sides have moved on.
Normal diplomatic relations have resumed and French plans are allowed to fly over the country to reach army bases in sub-Saharan Africa.
Mr Macron, on his second visit to Algeria since he took power in 2017, "has chosen to direct this visit towards the future — start-ups, innovation, youth, new sectors," his office said.
Algerian media said his visit showed both countries' desire for relations built around "a new vision based on equal treatment and balance of interests".
Mr Tebboune said he and Mr Macron had discussed how to bring stability to Libya and the Sahel region.
They are also expected to discuss boosting Algerian gas deliveries to Europe to fill the vast shortfall after Russia's invasion of Ukraine in February.
European nations want to end their dependence on Russian hydrocarbons, giving Algeria — Africa's biggest gas exporter, with direct pipelines to Spain and Italy — renewed influence.
"The French president will certainly ask Algeria to make an effort to try to increase its gas production," said Algerian economist Abderrahmane Mebtoul.
Mr Macron's office has said gas is not a major feature of the visit, although the head of French energy company Engie, Catherine MacGregor, is in his delegation.
Emmanuel Macron recognises 1962 massacre in Algeria - video
Mr Macron has long ruled out issuing an apology for the highly sensitive issue of colonialism, but he has made gestures aimed at healing past wounds.
In Algiers, few have much sympathy for the French president, who during his first election campaign described his country's colonialism as a "crime against humanity".
"Before he was president, he used nice words," said computer scientist Othmane Abdellouche, 62. "He visited, but right after he went back to France he changed
"He used a totally different discourse."
But businessman Kamel Moula, who leads the Council of Algerian Economic Renewal, told the TSA news website that he wanted to see "a new mode of co-operation" between the two countries that would allow them to "jointly conquer new markets".
French historians say half a million civilians and combatants died during Algeria's bloody war for independence, 400,000 of them Algerian.
The Algerian authorities say 1.5 million were killed.
Mr Tebboune's office said in October that more than 5.6 million Algerians were killed during the colonial period.
Algerian human rights groups have urged Mr Macron not to overlook abuses by the government that came to power after long-time leader Abdelaziz Bouteflika stepped down in 2019.
Mr Tebboune, a prime minister under Mr Bouteflika, has clamped down on the Hirak opposition movement that forced his predecessor to resign.