diff --git a/assets/css/components.css b/assets/css/components.css
index efd63c08c..9d2da14b8 100644
--- a/assets/css/components.css
+++ b/assets/css/components.css
@@ -54,11 +54,11 @@
   }
 
   .icon-button {
-    @apply p-1 flex items-center justify-center text-gray-400 hover:text-gray-800;
+    @apply p-1 flex items-center justify-center text-gray-400 hover:text-gray-800 rounded-full;
   }
 
   .icon-button:focus {
-    @apply rounded-full bg-gray-100;
+    @apply bg-gray-100;
   }
 
   .icon-button i {
diff --git a/assets/css/js_interop.css b/assets/css/js_interop.css
index 0ffa25a7d..4a80d88e5 100644
--- a/assets/css/js_interop.css
+++ b/assets/css/js_interop.css
@@ -121,3 +121,7 @@ solely client-side operations.
 [data-element="clients-list-item"][data-js-followed] [data-meta="follow"] {
   @apply hidden;
 }
+
+[phx-hook="VirtualizedLines"]:not(:hover) [data-clipboard] {
+  @apply hidden;
+}
diff --git a/assets/js/virtualized_lines/index.js b/assets/js/virtualized_lines/index.js
index fff23bab6..48de1ba1c 100644
--- a/assets/js/virtualized_lines/index.js
+++ b/assets/js/virtualized_lines/index.js
@@ -23,6 +23,8 @@ import { getLineHeight } from "../lib/utils";
  *
  *   * one annotated with `data-content` where the visible elements are rendered,
  *     it should contain any styling relevant for the container
+ *
+ * Also a `data-clipboard` child button is used for triggering copy-to-clipboard.
  */
 const VirtualizedLines = {
   mounted() {
@@ -62,6 +64,18 @@ const VirtualizedLines = {
       this.state.contentElement,
       config
     );
+
+    this.el
+      .querySelector("[data-clipboard]")
+      .addEventListener("click", (event) => {
+        const content = Array.from(this.state.templateElement.children)
+          .map((child) => child.innerText)
+          .join("");
+
+        if ("clipboard" in navigator) {
+          navigator.clipboard.writeText(content);
+        }
+      });
   },
 
   updated() {
diff --git a/lib/livebook_web/live/output/text_component.ex b/lib/livebook_web/live/output/text_component.ex
new file mode 100644
index 000000000..99f6b487c
--- /dev/null
+++ b/lib/livebook_web/live/output/text_component.ex
@@ -0,0 +1,29 @@
+defmodule LivebookWeb.Output.TextComponent do
+  use LivebookWeb, :live_component
+
+  @impl true
+  def render(assigns) do
+    ~L"""
+    <div id="virtualized-text-<%= @id %>"
+      class="relative"
+      phx-hook="VirtualizedLines"
+      data-max-height="300"
+      data-follow="<%= @follow %>">
+      <div data-template class="hidden">
+        <%= for line <- ansi_to_html_lines(@content) do %>
+          <%# Add a newline, so that multiple lines can be copied properly %>
+          <div><%= [line, "\n"] %></div>
+        <% end %>
+      </div>
+      <div data-content class="overflow-auto whitespace-pre font-editor text-gray-500 tiny-scrollbar"
+        id="virtualized-text-<%= @id %>-content"
+        phx-update="ignore"></div>
+      <div class="absolute right-4 top-0 z-10">
+        <button class="icon-button bg-gray-100" data-clipboard>
+          <%= remix_icon("clipboard-line", class: "text-lg") %>
+        </button>
+      </div>
+    </div>
+    """
+  end
+end
diff --git a/lib/livebook_web/live/session_live/cell_component.ex b/lib/livebook_web/live/session_live/cell_component.ex
index fdd22bddd..0c0ef643d 100644
--- a/lib/livebook_web/live/session_live/cell_component.ex
+++ b/lib/livebook_web/live/session_live/cell_component.ex
@@ -286,15 +286,22 @@ defmodule LivebookWeb.SessionLive.CellComponent do
   end
 
   defp render_output(_socket, text, id) when is_binary(text) do
-    text
     # Captured output usually has a trailing newline that we can ignore,
     # because each line is itself an HTML block anyway.
-    |> String.replace_suffix("\n", "")
-    |> render_virtualized_output(id, follow: true)
+    text = String.replace_suffix(text, "\n", "")
+    live_component(LivebookWeb.Output.TextComponent, id: id, content: text, follow: true)
   end
 
   defp render_output(_socket, {:text, text}, id) do
-    render_virtualized_output(text, id)
+    live_component(LivebookWeb.Output.TextComponent, id: id, content: text, follow: false)
+  end
+
+  defp render_output(_socket, {:image, content, mime_type}, id) do
+    live_component(LivebookWeb.Output.ImageComponent,
+      id: id,
+      content: content,
+      mime_type: mime_type
+    )
   end
 
   defp render_output(_socket, {:vega_lite_static, spec}, id) do
@@ -315,14 +322,6 @@ defmodule LivebookWeb.SessionLive.CellComponent do
     )
   end
 
-  defp render_output(_socket, {:image, content, mime_type}, id) do
-    live_component(LivebookWeb.Output.ImageComponent,
-      id: id,
-      content: content,
-      mime_type: mime_type
-    )
-  end
-
   defp render_output(_socket, {:error, formatted}, _id) do
     render_error_message_output(formatted)
   end
@@ -334,29 +333,6 @@ defmodule LivebookWeb.SessionLive.CellComponent do
     """)
   end
 
-  defp render_virtualized_output(text, id, opts \\ []) do
-    follow = Keyword.get(opts, :follow, false)
-    lines = ansi_to_html_lines(text)
-    assigns = %{lines: lines, id: id, follow: follow}
-
-    ~L"""
-    <div id="<%= @id %>"
-      phx-hook="VirtualizedLines"
-      data-max-height="300"
-      data-follow="<%= follow %>">
-      <div data-template class="hidden">
-        <%= for line <- @lines do %>
-          <%# Add a newline, so that multiple lines can be copied properly %>
-          <div><%= [line, "\n"] %></div>
-        <% end %>
-      </div>
-      <div data-content class="overflow-auto whitespace-pre font-editor text-gray-500 tiny-scrollbar"
-        id="<%= @id %>-content"
-        phx-update="ignore"></div>
-    </div>
-    """
-  end
-
   defp render_error_message_output(message) do
     assigns = %{message: message}