macOS Catalina requires apps to be notarized by Apple. Your version of Visual Studio Code is yet to be updated by Microsoft for the new OS.
Please try the following:
Right-click on the app and select Open.
If this did not work, remove the quarantine extended attribute that’s set on the app:
- Move the app to the Applications folder
- Open Terminal.app, then paste and execute the following command:
xattr -d com.apple.quarantine /Applications/Visual\ Studio\ Code.app
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✔︎ solved
Feb. 2020, now that VSCode 1.42 has been released, vscode commit c196df9 from João Moreno is supposed to solve this issue; from PR 86588.
Notarized macOS Builds
Visual Studio Code for macOS is finally notarized, so you should no longer see the following dialog: