The new penal law, seen by Reuters on Tuesday, is dated Aug. 17 but was officially published over the weekend. It will come into force 90 days after publication, the document said.
Obiang's son, Vice-President Teodoro Nguema Obiang Mangue, described the abolition as "historical and memorable."
"I write it with capital letters to seal this unique moment," he tweeted on Monday. "EQUATORIAL GUINEA HAS ABOLISHED THE DEATH PENALTY."
Amnesty International says the last executions there took place in the tiny, oil-producing state in 2014. Obiang had said in 2019 that he would propose a law to end capital punishment.
With a population of about 1.4 million split between a mainland on the Central African coast and an island in the Gulf of Guinea, Equatorial Guinea has a poor record on human rights. Campaign groups and foreign powers have accused the Obiang government of torture, arbitrary detentions and sham trials.
Obiang, 80, has ruled Equatorial Guinea, a former Spanish colony, since he seized power in a coup in 1979, making him the world's longest-serving president in office.
Obiang Mangue was tried in absentia and convicted of embezzlement by a French court in 2020 in relation to luxury assets seized in France, including a mansion in the heart of Paris. He denies any wrongdoing.
Capital punishment remains legal in just over 30 African countries, but more than 20 of those have not carried out executions for at least 10 years, according to data provider Statista.