UPDATE Jan 2021: WebView2 has been released. This enables integration of the Chromium based Edge as a web control. It's a lot more complicated to use, unfortunately, but a lot more powerful. Works with WinForms or WPF or C++ apps.
https://docs.microsoft.com/en-us/microsoft-edge/webview2/
UPDATE May 2018: FINALLY Microsoft has made it easy.
https://blogs.windows.com/msedgedev/2018/05/09/modern-webview-winforms-wpf-apps/
For now, the new control is in the Windows Community Toolkit 3.0 and contained in Toolkit.Win32.UI.Controls.dll, which you may need to manually add a reference to.
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I wish somebody had mentioned this, so I'll add this because it doesn't look like webbrowser control will ever be updated.
Use the WebView control instead. This uses EdgeHTML rendering engine. This is part of WindowPresentation layer but it is possible to link from WinForms and presumably other apps. You must convert to a UWP app
import Windows.UI.Xaml.Controls.WebView
Example code: https://code.msdn.microsoft.com/windowsapps/XAML-WebView-control-sample-58ad63f7
I haven't replaced my WebBrowser with WebView yet, but the interface looks pretty familiar.
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