Djerad, 65, succeeds Sabri Boukadoum, who held the post temporarily after the resignation of Noureddine Bedoui on 19 December.
The new premier served in the administration of a previous president in the 1990s, but was sidelined by longtime leader Abdelaziz Bouteflika, who was ousted in April.
The massive street protest movement that prompted Bouteflika to step down has rejected Tebboune's election this month as illegitimate. The opposition boycotted the vote, with less than 40 percent turning out to cast their ballot.
The protesters rejected any election that took place while the military stayed involved in politics and Bouteflika-era figures retained powerful positions.
Algeria's authorities publicly welcomed the street protests, casting them as a patriotic movement aimed at refreshing Algerian politics and ending corruption.
Djerad spoke several times on radio after the protests began, backing them and demanding that Bouteflika and his allies quit power.
Tebboune's ascent to power was orchestrated by the veteran army chief Ahmed Gaid Salah who died last week from a heart attack at the age of 79.
The opposition say the ultimate power remains with the army.
(with agencies)
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