Monday’s elections mark the first time in 38 years Zimbabweans will not see 94-year-old Mr Mugabe’s name on the ballot paper.
Voter turnout in the presidential elections are expected to be high, with one poll by Afrobarometer indicating 85 percent of people are expected to have their say.
President Emmerson Mnangagwa, 75, is the front-runner with his party ZANU-PF, which he took over in 2014 after Mr Mugabe was expelled.
He faces opposition from challenger Nelson Chamisa, 40, and his Movement for Democratic Change (MDC) party.
It was previously led by long-term Mugabe opponent Morgan Tsvangirai until his death last year.
What time do polling stations open? When do they close?
Polls will open at 7am local time (6am BST) and close on 7pm (6pm BST) on Monday, July 30.
There are 23 candidates running for power but the race is likely to be a straight run between Mr Mnangagaw and lawyer Mr Chamisa.
Who is Robert Mugabe backing?
In a surprise move, Mr Mugabe has said he hopes his former allies in the military government will lose the election.
In a rambling, one-hour speech on Sunday, he said: “I can’t vote for ZANU-PF, what is left?
“I think it is just Chamisa.”
The frail-looking figure also stated: “I hope the choice of voting tomorrow will throw, thrust away the military government and bring us back to constitutionality.
“Let tomorrow be the voice of the people to say never again shall we experience a period where the army is used to thrust one person into power.”
Campaigning has been largely peaceful despite an explosion at one of President Mnangagawa’s campaign rallies last month in Bulawayo.
At least two people died and dozens more were injured in the blast.
Mnangagwa vs Chamisa – who will win?
Mr Mnangagwa is the current favourite, having ruled since last November when Mr Mugabe and his wife Grace were thrusted out of power.
He is known as “the crocodile” for his ruthlessness and has been accused of the same war crimes as Mr Mugabe when he was his right-hand man.
But challenger Mr Chamois has been criticised as being too young and inexperienced for the role, according to some Zimbabweans.
Voter Amanda Nash told the Financial Times: “He’s too young for it.
“We need someone who has been in government for some time to sort out our problems.”