The leaders have also agreed to set up a free trade zone and build a 847 kilometer (526 mile) road that will link the Algerian town of Tindouf to Mauritania's Ezouirat.
"Hotels, restaurants, taxi drivers and workers in the public sector and housing sectors are happy," Dida Abdewahab, a Tindouf resident, told Reuters.
The agreement comes a few days after OPEC member Algeria announced it would invest $442 million in energy projects in Mali, Niger and Libya.
Algeria has also announced it will open four other free trade zones in 2024 with Mali, Niger, Tunisia and Libya.
Algeria, heavily dependent on oil and gas sales, is striving to diversify its economy. Its exports outside hydrocarbons reached a record of $7
billion in 2022, and totaled $5.3 billion in the first 11 months of 2023, according to official figures.
Algeria has a trade surplus in ceramics, clinker cement, ferrous products, refined sugar, and dates.
"This should have happened a long time ago but there was not enough diplomatic attention given to Mauritania," Geoff Porter, an American analyst specialized in North Africa, told Reuters.