Zimbabwe's Robert Mugabe resigns, ending 37-year rule
Mr Mugabe, 93, was until now the world's oldest leader. He had previously refused to resign despite last week's military takeover and days of protests.
The letter did not mention who would take over from Mr Mugabe, who has been in power since independence in 1980.
The constitution says it should be the current vice-president, Phelekezela Mphoko, a supporter of Grace Mugabe, Mr Mugabe's wife.
Mr Mudenda said moves were under way to ensure a new leader could take over by late on Wednesday.
UK Prime Minister Theresa May said Mr Mugabe's resignation "provides Zimbabwe with an opportunity to forge a new path free of the oppression that characterised his rule".
She said that former colonial power Britain, "as Zimbabwe's oldest friend", will do all it can to support free and fair elections and the rebuilding of the Zimbabwean economy.
Opposition leader Morgan Tsvangirai told the BBC he hoped that Zimbabwe was on a "new trajectory" that would include free and fair elections. He said Mr Mugabe should be allowed to "go and rest for his last days".