It leaves Facebook searching for a replacement head of UK PR and comms when Tobias, who will also be responsible for the Middle East and Africa, takes up her new role next Monday.
The role is the first new comms position outside the US at Instagram and reports directly to US-based head of PR David Swain.
Tobias is charged with setting up Instagram's PR function across the region with a wide-ranging remit that includes media and analyst relations, as well as reactive and proactive PR.
Tobias will support existing agency relationships in countries such as the UK, Russia and Germany, and look at new agency partnerships for other key markets that are in the process of being defined.
Instagram is attempting to build momentum in key verticals such as fashion, sport, food and celebrities as it seeks to build its global user base of 150 million.
It has already started to build its European fashion connections. Founder Kevin Systrom came to London Fashion Week in September to discuss the future of Instagram with model Lily Cole and attend the Burberry catwalk show.
Tobias said her remit would include comms around the potential rollout of advertising on the service in Europe following its introduction in the US.
Having similarly set up the PR functions within Facebook in the UK and previously at eBay for Gumtree where she was head of comms, Tobias commented: "It is a great opportunity for me and I am really excited to be taking the role on."
Facebook's European corporate comms director Stefano Hesse will begin the search to fill the position vacated by Tobias, and will be the first point of contact in the UK in the interim, with support from its UK agencies.