diff --git a/Userland/Libraries/LibWeb/Fetch/Infrastructure/HTTP/Bodies.cpp b/Userland/Libraries/LibWeb/Fetch/Infrastructure/HTTP/Bodies.cpp
index 0037d3548e9d6..4287e2462d389 100644
--- a/Userland/Libraries/LibWeb/Fetch/Infrastructure/HTTP/Bodies.cpp
+++ b/Userland/Libraries/LibWeb/Fetch/Infrastructure/HTTP/Bodies.cpp
@@ -1,10 +1,12 @@
 /*
  * Copyright (c) 2022-2023, Linus Groh <linusg@serenityos.org>
+ * Copyright (c) 2024, Jelle Raaijmakers <jelle@ladybird.org>
  *
  * SPDX-License-Identifier: BSD-2-Clause
  */
 
 #include <LibJS/Runtime/PromiseCapability.h>
+#include <LibWeb/Bindings/ExceptionOrUtils.h>
 #include <LibWeb/Bindings/MainThreadVM.h>
 #include <LibWeb/Fetch/BodyInit.h>
 #include <LibWeb/Fetch/Infrastructure/HTTP/Bodies.h>
@@ -12,7 +14,6 @@
 #include <LibWeb/Fetch/Infrastructure/Task.h>
 #include <LibWeb/HTML/Scripting/TemporaryExecutionContext.h>
 #include <LibWeb/Streams/AbstractOperations.h>
-#include <LibWeb/WebIDL/Promise.h>
 
 namespace Web::Fetch::Infrastructure {
 
@@ -70,38 +71,37 @@ void Body::fully_read(JS::Realm& realm, Web::Fetch::Infrastructure::Body::Proces
     VERIFY(!task_destination.has<Empty>());
     auto task_destination_object = task_destination.get<JS::NonnullGCPtr<JS::Object>>();
 
-    // 2. Let successSteps given a byte sequence bytes be to queue a fetch task to run processBody given bytes, with taskDestination.
-    auto success_steps = [&realm, process_body, task_destination_object = task_destination_object](ReadonlyBytes bytes) -> ErrorOr<void> {
-        // Make a copy of the bytes, as the source of the bytes may disappear between the time the task is queued and executed.
-        auto bytes_copy = TRY(ByteBuffer::copy(bytes));
-        queue_fetch_task(*task_destination_object, JS::create_heap_function(realm.heap(), [process_body, bytes_copy = move(bytes_copy)]() mutable {
-            process_body->function()(move(bytes_copy));
+    // 2. Let successSteps given a byte sequence bytes be to queue a fetch task to run processBody
+    //    given bytes, with taskDestination.
+    auto success_steps = [&realm, process_body, task_destination_object = task_destination_object](ByteBuffer bytes) {
+        queue_fetch_task(*task_destination_object, JS::create_heap_function(realm.heap(), [process_body, bytes]() mutable {
+            process_body->function()(move(bytes));
         }));
-        return {};
     };
 
-    // 3. Let errorSteps optionally given an exception exception be to queue a fetch task to run processBodyError given exception, with taskDestination.
-    auto error_steps = [&realm, process_body_error, task_destination_object](JS::GCPtr<WebIDL::DOMException> exception) {
+    // 3. Let errorSteps optionally given an exception exception be to queue a fetch task to run
+    //    processBodyError given exception, with taskDestination.
+    auto error_steps = [&realm, process_body_error, task_destination_object](JS::Value exception) {
         queue_fetch_task(*task_destination_object, JS::create_heap_function(realm.heap(), [process_body_error, exception]() {
             process_body_error->function()(exception);
         }));
     };
 
-    // 4. Let reader be the result of getting a reader for body’s stream. If that threw an exception, then run errorSteps with that exception and return.
+    // 4. Let reader be the result of getting a reader for body’s stream. If that threw an
+    //    exception, then run errorSteps with that exception and return.
+    HTML::TemporaryExecutionContext execution_context { realm, HTML::TemporaryExecutionContext::CallbacksEnabled::Yes };
+    auto reader_or_exception = Streams::acquire_readable_stream_default_reader(*m_stream);
+    if (reader_or_exception.is_exception()) {
+        auto throw_completion = Bindings::dom_exception_to_throw_completion(realm.vm(), reader_or_exception.release_error());
+        error_steps(throw_completion.release_value().value());
+        return;
+    }
+    auto reader = reader_or_exception.release_value();
+
     // 5. Read all bytes from reader, given successSteps and errorSteps.
-    // FIXME: Use streams for these steps.
-    m_source.visit(
-        [&](ByteBuffer const& byte_buffer) {
-            if (auto result = success_steps(byte_buffer); result.is_error())
-                error_steps(WebIDL::UnknownError::create(realm, "Out-of-memory"_string));
-        },
-        [&](JS::Handle<FileAPI::Blob> const& blob) {
-            if (auto result = success_steps(blob->raw_bytes()); result.is_error())
-                error_steps(WebIDL::UnknownError::create(realm, "Out-of-memory"_string));
-        },
-        [&](Empty) {
-            error_steps(WebIDL::DOMException::create(realm, "DOMException"_fly_string, "Reading from Blob, FormData or null source is not yet implemented"_string));
-        });
+    reader->read_all_bytes(
+        JS::create_heap_function(realm.heap(), move(success_steps)),
+        JS::create_heap_function(realm.heap(), move(error_steps)));
 }
 
 // https://fetch.spec.whatwg.org/#body-incrementally-read