Beddoes, whose party has only two seats in the 71-member parliament, replaces Fiji Labour Party head Mahendra Chaudhry.
The move came after Labour accepted an offer of nine Cabinet seats in the multiparty government, effectively making it part of the nationalist-dominated government.
The 35-member Cabinet of Prime Minister Laisenia Qarase is the biggest in Fiji's history and the first to combine the governing party with the major opposition party, the AP reports.
The power-sharing deal has boosted expectations that racial tensions will cool following three coups in the past 19 years sparked by disputes between ethnic Fijians and ethnic Indians.
Chaudhry became Fiji's first ethnic Indian prime minister in 1999 before being forced from office by an armed nationalist coup in May 2000.
In last month's elections, Chaudhry's predominantly Indo-Fijian party narrowly lost to the ruling indigenous Fijian-dominated Soqosoqo Duavata Ni Lewenivanua (SDL) Party. SDL won 36 seats, Labour 31, UPP two and independents two in the 71-member parliament.
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