This isn’t quite right. On his first day in office, President Obama signed a memorandum on open government focused transparency, public participation, and collaboration, which instructed the CTO, GSA & head of OMB to draft an Open Government Directive: https://obamawhitehouse.archives.gov/the-press-office/transparency-and-open-government
Subsequent executive orders issued by mayors and governors generally drew more upon on the Directive, issued in December 2009, specifically the section regarding publishing information online: https://obamawhitehouse.archives.gov/open/documents/open-government-directive
…though I see most policies in recent years drawn from other policies: https://www.opendatapolicies.org
A 2013 memorandum was specifically focused on open data and served as a rough framework for the Open Government Data Act in Congress.