In the elections held the following year under the Internal Settlement terms , boycotted by ZANU and ZAPU , Muzorewa won a majority , and became the first Prime Minister of the reconstituted , majority @-@ ruled state of Zimbabwe Rhodesia on 1 June 1979 . This new order failed to win international acceptance , however , and in December 1979 the Lancaster House Agreement was agreed in London by Zimbabwe Rhodesia , the UK government and the Patriotic Front , returning the country to its former colonial status . The UK government suspended the constitution and took direct control for an interim period . Fresh elections were won by Mugabe , who took power in April 1980 , concurrently with the country 's recognised independence as Zimbabwe .