A letter from Mr Mugabe said that the decision was voluntary and that he had made it to allow a smooth transition of power.
The surprise announcement halted an impeachment hearing that had begun against him.
Lawmakers roared in jubilation and people have begun celebrating in the streets.
Mugabe 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.
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 Britain, “as Zimbabwe’s oldest friend”, will do all it can to support free and fair elections and the rebuilding of the Zimbabwean economy.
Robert Mugabe has been in power since independence in 1980. Mr Mugabe has won elections, but over the past 15 years these have been marred by violence against political opponents.
He has presided over a deepening economic crisis in Zimbabwe, where people are on average 15% poorer now than they were in 1980.
“I am the happiest person under the sun right now, because I always believed that Mugabe was going to step down in my lifetime and it has happened,” human rights activist Linda Masarira told the BBC.
“And now going forward it’s time for the opposition to reorganise and ensure that we will have a government that cares for the people. And everyone has to be included.”
What triggered the moves to oust him was his dismissal of Emmerson Mnangagwa as vice-president two weeks ago.
That decision was seen by many as clearing the way for Grace Mugabe to succeed her husband as leader. It riled the military leadership, who stepped in and put Mr Mugabe under house arrest. (Courtesy BBC)