Bouteflika, who was re-elected by a landslide in last month's leadership contest despite grave concerns about his health, had already reappointed Sellal as his prime minister, after the latter stepped down in February to run his election campaign.
"The president, after consulting the prime minister... issued a decree naming members of his government," the presidency said in a statement.
The 34-member cabinet dominated by technocrats also includes seven women.
The key portfolios being retained are Ramtane Lamamra (foreign affairs), Yayeb Belaiz (interior), Tayb Louh (justice), Youcef Yousfi (energy) and General Ahmed Gaid-Salah as deputy defence minister.
Another figure leaving the cabinet is culture minister Khalida Toumi, a former opposition member and leading Algerian feminist who eventually rallied behind Bouteflika, joining his government in 2002.
She will be succeeded by Nadia Labidi, a professor at Algiers university, with another woman and university teacher, Nouria Benghebrit, heading the education ministry.