The two countries share the Greater Tortue Ahmeyim (GTA) offshore natural gas field.
It was jointly developed by British energy giant BP, American company Kosmos Energy, Mauritanian hydrocarbons company SMH, and Senegal's state-owned Petrosen.
It aims to produce around 2.5 million tonnes of liquefied natural gas per year.
The start of production was initially expected in late 2024 but was pushed back to this year.
"The achievement of this important milestone marks a major step towards the completion of the GTA project," the two countries said in a joint statement.
The opening of the first gas well "paves the way for the start of the commercialisation of the gas planned very soon", they added.
Senegal, ranked among the 25 least developed countries in the world, joined the club of oil producers in June last year when production began at the Sangomar offshore oil field, operated by Australian group Woodside Energy.
Senegalese President Bassirou Diomaye Faye, who swept to victory in March on a promise of radical reform, declared an audit of the oil, gas and mining sectors as one of his first announcements as head of state.
He vowed in a New Year's speech late Tuesday to guarantee the "optimal and transparent exploitation of oil and gas resources for the benefit of the national economy and current and future generations".
