Bind Angularjs to newly created html element dynamically

One solution would be to use ngInclude with $templateCache, as demonstrated in this Plunker.

There are a couple things to note.

The first is that you can fetch your template using a service and add it to the $templateCache, as described here (example copied):

myApp.service('myTemplateService', ['$http', '$templateCache', function ($http, $templateCache) {
  $http(/* ... */).then(function (result) {
    $templateCache.put('my-dynamic-template', result);
  });
}]);

Then you can include it in your template as follows:

<div ng-include="'my-dynamic-template'"></div>

ngInclude will allow databinding on the html string, so you don’t need ngBindHtml.

The second is that, as ngInclude creates a new scope, accessing the html property outside of the newly created scope won’t work properly unless you access it via an object on the parent scope (e.g. ng-model="data.html" instead of ng-model="html". Notice that the $scope.data = {} in the parent scope is what makes the html accessible outside of the ngInclude scope in this case.

(See this answer for more on why you should always use a dot in your ngModels.)

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Edit

As you pointed out, the ngInclude option is much less useful when using a service to return the HTML.

Here’s the edited plunker with a directive-based solution that uses $compile, as in David’s comment above.

The relevant addition:

app.directive('customHtml', function($compile, $http){
  return {
    link: function(scope, element, attrs) {
      $http.get('template.html').then(function (result) {
        element.replaceWith($compile(result.data)(scope));
      });
    }
  }
})