Solved (cross checked on Ubuntu 16.04 and CentOS 7):
In the VS Code menu, go into File / Preferences / Settings.
In the “Search settings” window, type omnisharp.path
Click on “Edit in settings.json” link.
Add (or edit) like this: “omnisharp.path”: “latest”
(from: https://github.com/OmniSharp/omnisharp-vscode/issues/2965)