The 93-year-old’s resignation followed the commencement of impeachment proceedings on Tuesday.
Mr. Mudenda announced that Mr. Mugabe resigned in a letter written to parliament and consequently suspended the impeachment proceedings.
Mr. Mugabe, who has ruled the southern African nation since 1980, was expected to announce his resignation on Sunday after his ruling ZANU-PF ousted him as leader. The party had given him 24 hours to resign as president or face impeachment.
In his nationally broadcast address to Zimbabwe, however, Mr. Mugabe defied expectations and said he would remain in power.
Last week, Zimbabwe’s military placed Mr. Mugabe under house arrest and urged him to resign peacefully.
The military takeover was prompted by Mr. Mugabe’s sacking of his vice president, Emmerson Mnangagwa, a move seen by many in the military as a purge intended to clear a path of succession for his wife, Grace Mugabe.
Military tanks rolled into the capital city of Harare on November 14, and the military announced the next day that the president had been placed under house arrest.
Mr. Mugabe has ruled Zimbabwe since the country gained independence in 1980. While seen by many across the continent as a heroic liberator and anti-colonialist, Mr. Mugabe drew criticism for his authoritarian grip on power and poor handling of the national economy.