According to the Zimbabwe Mail, High Court Judge Justice George Chiweshe ruled that "Operation Restore Legacy" was constitutionally permissible and lawful.
The impeachment process was initiated after he refused to resign till Monday afternoon, the deadline set by ruling ZANU-PF party.
Earlier, Zimbabwe's military seized power on Wednesday to force 93-year-old Mugabe out of office.
Wild celebrations broke out at a joint sitting of parliament when Speaker Jacob Mudenda announced Mugabe's resignation and suspended the impeachment procedure, reported The Telegraph.
The Speaker read out Robert Mugabe's resignation letter to the parliament.
"I Robert Gabriel Mugabe, in terms of Section 96 of the Constitution of Zimbabwe, hereby formally tender my resignation... with immediate effect," said Speaker Mudenda, reading the letter.
The Telegraph quoted the letter as saying that Mugabe was tendering his resignation to "allow a smooth transfer of power". The letter was read out in front of a cheering and dancing parliament.
The ruling party chose Emmerson Mnangagwa to replace Mugabe.
Mnangagwa, a veteran of the liberation war and for decades Mugabe's right-hand man, had earlier fled into exile after being sacked from his position and the Zanu-PF.
The proposal of the impeachment motion was drafted by ZANU-PF party, which had earlier expelled Mugabe from the party. Mugabe's 52-year-old wife has also been booted out from the party.
The impeachment motion said Mugabe is a "source of instability", has shown disrespect for the rule of law, and is to blame for an unprecedented economic tailspin over the past 15 years, and allowed his wife, Grace Mugabe, to "usurp constitutional power".(ANI)