In the callback for the GUI button , you can make a call to the WEB function to open a web browser for a given URL:
web('stackoverflow.com/');
For instance:
uicontrol('Style','pushbutton',... 'Position',[50 50 100 25],... 'String','Go to SO!',... 'Callback',@(hObject,eventData) web('stackoverflow.com/'));
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