“The decision followed a “peaceful, successful and credible” referendum on a new constitution earlier this month, the EU said in a statement.
However, sanctions will remain in force against 10 people – including Zimbabwe’s President Robert Mugabe – and two firms, EU sources say.
The EU imposed sanctions, including a travel ban, in 2002.
It said it was in response to human rights abuses and political violence under Mr Mugabe’s rule.
Allies of Mr Mugabe have long argued that the sanctions should be unconditionally removed and that they have had a negative impact on Zimbabwe’s economy.
Mr Mugabe, 89, and his rival, Prime Minister Morgan Tsvangirai, 61, have been sharing power since disputed elections marred by violence in 2008.
Zimbabweans overwhelmingly approved the new constitution – which expands civil liberties and has been endorsed by both Mr Mugabe and Mr Tsvangirai – in the 16 March referendum.