The memorandum sets out the rights and obligations of the EU observers.
The new government's "desire to have transparency in the election process (by) inviting different international observers so that they can come and observe our elections... and observe democracy in action," Moyo told journalists after the signing.
The head of the last European Union observer mission, Pierre Schori, was thrown out of Zimbabwe in 2002 on the eve of presidential elections that were condemned as flawed.
In the intervening years the EU did not send missions to other Zimbabwe polls as Mugabe held a firm grip on power until his downfall.
Mnangagwa, who has invited the EU and the Commonwealth among a host of foreign monitors to observe the vote, is a veteran hardliner from the ruling ZANU-PF party and was a long-time ally of Mugabe.
In addition to observing the run-up to the elections and election day itself, the observer mission will also monitor electoral complaints that may be lodged after the elections, the EU mission in Harare said in a statement.
Two US-funded pro-democracy groups on Monday also announced they were deploying observers for the first time to watch the Zimbabwe vote.
The National Democratic Institute and the International Republican Institute said in a statement they were deploying a joint mission "in response to President Emmerson Mnangagwa's public statements welcoming international observers to monitor the upcoming Zimbabwe elections".