Facebook has launched a tool that will enable members to transfer photos and videos they have uploaded to the platform to Google Photos.
The service would initially roll out in Ireland and then, in 2020, across the world, Facebook said.
It also said it planned to include other services in future as part of its commitment to "data portability".
The Open Rights Group campaign welcomed the move but said it needed to extend beyond the technology giants.
"It's important that Facebook and other companies allow you to move data about," said ORG director Jim Killock.
"It's critical that this kind of portability is not just for a handful of global giants, if it is going to encourage competition.
"There will also be potential privacy issues with data portability as users will potentially take risks when they move data to third parties, so companies and regulators will need to develop ways that deal with rogue actors."
In a blog post announcing the Google Photo tool, which has taken a year to build, Facebook said it had considered security risks.
"Any mechanism to send data outside of a service carries risk," it said.
"We have put measures in place to mitigate these risks."
These include extra authentication steps to ensure only the owner of the account can transfer a file.
Facebook's Google Photos tool is part of the Data Transfer Project, which aims to be an open-source platform anyone will be able to use to move their data between online services.
Apple, Google, Microsoft and Twitter are also involved in the collaboration.
Facebook has allowed members to download their data since 2010.
In 2018, journalist Radhika Sanghani told BBC News the 324MB data file of her 12 years on Facebook had taken 40 minutes to download.