However, Wefaq appeared unimpressed by the move.
Fahim Abdullah, a Wefaq official, said: "At the moment the rulers do not care about Sunnis or Shias, they just want their own interests as long as they have someone who obeys them."
Abdullah said that Oraied was close to the prime minister.
Wefaq won 17 of the parliament's 40 seats in last month's elections. It had boycotted the previous polls in protest at the introduction of the Shura council, an appointed body which has the same powers as the elected council.
King Hamad kept key portfolios unchanged in the new cabinet, according to the official Bahrain News Agency.
A new portfolio, oil and gas, was given to Abdul-Hussain bin Ali Mirza, the head of the National Oil and Gas Authority.
Non-OPEC Bahrain is the smallest oil producer among six Gulf Arab states grouped under the US-allied Gulf Cooperation Council.
Bahrain is home to the US Navy's Fifth Fleet, and is the region's main banking hub.
The Bahraini cabinet resigned on Sunday to make way for a new government after the parliamentary polls.
Last week, Bahrain appointed a 40-member Shura council with 20 Sunni Muslims and 10 women.