Add setting edit_history_visible_to_public to control whether post edits can be viewed by everyone. Uncheck it so only staff users can see edits.

app/assets/javascripts/discourse/models/post.js

@@ -343,7 +343,11 @@ Discourse.Post = Discourse.Model.extend({
     topic = this.get('topic');
     return !topic.isReplyDirectlyBelow(this);
 
-  }.property('reply_count')
+  }.property('reply_count'),
+
+  canViewEditHistory: function() {
+    return (Discourse.SiteSettings.edit_history_visible_to_public || (Discourse.User.current() && Discourse.User.current().get('staff')));
+  }.property()
 
 });
 

app/assets/javascripts/discourse/templates/post.js.handlebars

@@ -32,10 +32,17 @@
           <div class='topic-meta-data-inside'>
             {{#if hasHistory}}
               <div class='post-info edits'>
-                <a href='#' class="{{unbound historyHeat}}" {{action showHistory this}} title="{{i18n post.last_edited_on}} {{unboundDate updated_at}}">
-                  {{editCount}}
-                  <i class='icon-pencil'></i>
-                </a>
+                {{#if canViewEditHistory}}
+                  <a href='#' class="{{unbound historyHeat}}" {{action showHistory this}} title="{{i18n post.last_edited_on}} {{unboundDate updated_at}}">
+                    {{editCount}}
+                    <i class='icon-pencil'></i>
+                  </a>
+                {{else}}
+                  <span class="{{unbound historyHeat}}" title="{{i18n post.last_edited_on}} {{unboundDate updated_at}}">
+                    {{editCount}}
+                    <i class='icon-pencil'></i>
+                  </span>
+                {{/if}}
               </div>
             {{/if}}
             <div class='post-info'>

app/assets/stylesheets/application/topic-post.css.scss

@@ -390,7 +390,7 @@
       display: inline-block;
       margin-right: 12px;
       &.edits {
-        a, a:visited {
+        a, a:visited, span {
           color: #aaa;
         }
       }

app/models/site_setting.rb

@@ -87,6 +87,7 @@ class SiteSetting < ActiveRecord::Base
   setting(:apple_touch_icon_url, '/assets/default-apple-touch-icon.png')
 
   setting(:ninja_edit_window, 5.minutes.to_i)
+  client_setting(:edit_history_visible_to_public, true)
   client_setting(:delete_removed_posts_after, 24) # hours
   setting(:post_undo_action_window_mins, 10)
   setting(:system_username, '')

config/locales/server.en.yml

@@ -468,6 +468,7 @@ en:
     queue_jobs: "DEVELOPER ONLY! WARNING! By default, queue jobs in sidekiq. If disabled, your site will be broken."
     crawl_images: "Enable retrieving images from third party sources to insert width and height dimensions"
     ninja_edit_window: "Number of seconds after posting where edits do not create a new version"
+    edit_history_visible_to_public: "Allow everyone to see past versions of an edited post. If disabled, staff members are the only ones able to view edit history."
     delete_removed_posts_after: "Number of hours after which a post that was removed by its author will be deleted."
     max_image_width: "Maximum allowed width of images in a post"
     category_featured_topics: "Number of topics displayed per category in the /categories page"