301 Redirect only for posts

You’ll have to modify your old theme’s function.php. Add the following code:

function redirect_posts() {
    global $post;
    if ($post->post_type=='post') {
        return header('location:http://newblog.com/posts/'.$post->post_name);
    }
}
add_action('wp', 'redirect_posts');

The if codintion will check if the page what’s currently viewed is a post and it returns a header redirect to the new blog based on the old blog post’s slug.