The talks, which could begin as soon as next month, will try to increase trade and investment, and include a dialogue on human rights, officials said.
Since 1996, the EU has restricted its ties with Cuba to encourage multi-party democracy and progress on human rights.
The bloc is Cuba’s second-biggest trading partner after Venezuela.
It represents a major source of investment, and hundreds of thousands of European tourists visit the island every year.
EU foreign policy chief Catherine Ashton stressed that human rights remained “at the core” of its dealings with Cuba.
“These negotiations will help consolidate our engagement with Cuba,” she said. “I hope Cuba will take up this offer.”
The announcement comes with Cuba engaged in an economic and social reform process launched by President Raul Castro.
The EU ambassador to Havana, Herman Portocarero, said the aim was to support and accompany “change on the island” while also promoting human rights.
A legal bilateral relationship would bring “more opportunities”, he added.
The move indicates the most important diplomatic shift since the EU lifted sanctions against Cuba in 2008.
It follows the visit by Dutch Foreign Minister Frans Timmermans to Cuba in January. During his trip, Mr Timmermans called on the EU to change its policy toward the island.
He said the best way to promote change was through dialogue, not isolation.
In 1996, the EU agreed on a set of rules governing its relations with Cuba, called the Common Position.
It states that the EU’s objective is “to encourage a process of transition to a pluralist democracy and respect for human rights and fundamental freedoms, as well as sustainable recovery and improvement in the living standards of the Cuban people”.
Despite the policy, more than half of EU member states have bilateral agreements with Cuba.
Cuba has rejected the Common Position, arguing that it constitutes an interference in its internal affairs.