Ansip said proposed new EU legislation to tackle unnecessary restrictions on where data can be stored are likely to be published this autumn.
The proposals will also look to make it easier for businesses to move their data between rival cloud providers and ensure that public sector bodies can access data held by authorities in another EU country to help support digital public services, he said.
In a speech in Tallinn on Monday, Ansip said "there is no place" for rules requiring data to be stored "within national territory" in the EU. However, he said that data localisation measures may stem from "a lack of legal certainty about applicable rules and practices when it comes to data movement" and "a lack of trust in cross-border storage and processing of data".
The European Commission will propose new laws to address those issues, he said.
"One way forward would be to establish free movement of data as a basic principle in EU law," Ansip said. "We are also working on other principles in this package such as the principle of availability of data, even when it is stored in other EU countries, when public authorities need it. This could be for taxation or business register purposes, for example. And we are looking into improving the situation for switching cloud service providers. The main idea is that the user should be able to transfer data fast and without re-entering it manually."
"Commission experts are now working on an impact assessment, which is a necessary step before making any legal proposal. On that basis, we would prepare such a proposal, with the aim of presenting it this autumn. As we know, it is often not easy to draw the line between where personal data ends and non-personal data begins. That is why our starting point is the EU's recent General Data Protection Regulation," he said.
Removing "needless national and local barriers to data flows" and addressing "the underlying uncertainties" will benefit companies, governments and consumers, Ansip said.
"In the end, people, businesses and public administrations must be able to go digital with confidence," the commissioner said. "Sorting out today's situation would send a clear political message that Europe is open for business. That will be essential as we build a cross-border and data-focused economy."
Ansip pledged to combat unjustified controls on where data can be stored by organisations in the EU last autumn. The Commission subsequently published a paper in January which outlined options for liberating data so as to boost the EU economy.