The 21-year-old told BBC Sport last year that he was considering an approach from Algeria.
The Lille striker was born in France and played for them at every youth level from under-16 but is eligible for Algeria through his parents.
The Algeria Football Federation said it "will immediately begin the process of registering the player with Fifa."
The federation added Benzia met its president Mohamed Raouraoua this week to finalise his choice to play for the Desert Foxes.
Even though Fifa is yet to receive Benzia's request for a switch of nationality, the Algerian football authority is confident of a swift approval by the game's governing body.
Benzia has scored 26 goals in 43 appearances during his time playing for France's youth teams.
His capture will come as a morale boost for Algeria after they were snubbed by Lyon striker Nabil Fekir last year.
Benzia started his career at Lyon where he progressed from the academy to the senior squad and made his senior debut against Nice in May 2012.
He switched to Ligue 1 rivals Lille in August 2015 in search of regular football and has already scored five goals in 20 appearances for the club this season.

Mr Rouhani is expected to secure valuable trade deals following the lifting of international sanctions over Iran's nuclear programme.
Among them is a likely agreement with French aircraft manufacturer Airbus for more than 100 new aircraft.
Mr Rouhani will also meet French President Francois Hollande.
Mr Rouhani's five-day visit to Italy and France is the first by an Iranian president in nearly two decades, as the Iranian president seeks to rebuild economic ties and secure new trade deals.
Iran is likely to need hundreds of new aircraft in the coming years as it re-establishes commercial air travel restricted by the sanctions, and French carmakers will once again be free to supply to the Islamic Republic.
As well as a deal for Airbus planes, contracts are likely to be signed with car manufacturers Peugeot and Renault, Mr Rouhani told reporters on Monday.
In Italy, Mr Rouhani met with President Matteo Renzi and Pope Francis. Monday saw contracts worth around €17bn ($18.4bn; £12bn) signed between Iranian and Italian companies.
At Rome's Capitoline Museum, where Mr Rouhani and Mr Renzi met, nude statues were covered up and wine was removed from official menus out of respect for the Islamic Republic's strict laws governing propriety.
Iranian diplomats reportedly requested that no wine be served at Mr Rouhani's lunch meeting with Mr Hollande, leading French officials to postpone the meeting until after lunch.
During their meeting, Pope Francis urged Iran to work with other Middle Eastern countries against terrorism and arms trafficking, the Vatican said.
Iran has been accused of funding militant groups, such as Hezbollah in Lebanon.
Mr Rouhani asked the pontiff to pray for him, and gave him the gift of a hand-made carpet.

The boy identified as Che Labastide-Wellington, from Harrow, was at a party in Belvedere Way, Kenton, on Saturday evening.
Police said there had been a fight with a group of youths who tried to gain entry,
Che was stabbed in a later scuffle in an alleyway at about 00:30 GMT.
He was pronounced dead about an hour later.
More on this story and news from London
A 16-year-old boy was also stabbed and taken to a north London hospital for treatment. His remains in a stable condition, said police.
They said Che had been invited to the party, which appeared to be "a well-run event with appropriate adults in attendance".
They believed he was not involved in an early altercation with a group of youths denied entry to the party.
But he appeared to have been targeted later, a spokesman said.
Det Chief Insp Chris Jones said he wanted to speak to anyone who was near the alleyway between Belvedere Way and Tylers Gate when Che was stabbed.
A man aged 21 has been arrested on suspicion of murder and taken to a west London police station for questioning.
Two boys aged 15 and 16 were also arrested on suspicion of murder and bailed until mid-December.
A third, aged 14, is being held on suspicion of possession of an offensive weapon.
Former France youth international striker Yassine Benzia has pledged his senior future to Algeria.
[NEXT_CONCEPT]
Iranian president Hassan Rouhani will arrive in France on Wednesday for the second leg of his state visit to Europe, after three days in Italy.
[NEXT_CONCEPT]
A 17-year-old boy who was fatally stabbed in north-west London was at a 16th birthday party targeted by gatecrashers, police say.