Custom comment form in WordPress

I would like to customize the output of comment_form() function in WordPress.
To edit fields and textarea, I used the following code and all works fine.

<?php
    $req = get_option( 'require_name_email' );
    $fields =  array(
            // redefine author field
        'author' => '<p class="comment-form-author">' . '<label for="author">' . __( 'Name:' ) . ( $req ? ' <span class="required">*</span>' : '' ) . '</label>' .
        '<div class="input-prepend"><span class="add-on"><i class="icon-user"></i></span><input id="author" name="author" type="text" value="' . esc_attr( $commenter['comment_author'] ) . '" size="30"' . 'aria-required="true"' . ' required /></p>',
        'email'  => '<p class="comment-form-email"><label for="email">' . __( 'Email Address:' ) . ( $req ? ' <span class="required">*</span><br/>' : '' ) . '</label>' . 
        '<div class="input-prepend"><span class="add-on"><i class="icon-envelope"></i></span><input required id="email" name="email" type="text" value="' . esc_attr(  $commenter['comment_author_email'] ) . '" size="30"' . 'aria-required="true"' . ' required /></div></p>',
        'url'  => '<p class="comment-form-url"><label for="url">' . __( 'Your Website:' ) . '</label>' . 
        '<div class="input-prepend"><span class="add-on"><i class="icon-globe"></i></span><input id="url" name="url" type="text" value="' . esc_attr( $commenter['comment_author_url'] ) . '" size="30" /></div></p>'
        );
    $comments_args = array(
        'fields' => $fields,
            // redefine your own textarea (the comment body)
        'comment_field' => '<p class="comment-form-comment"><label for="comment">' . 'Comment' . '</label><textarea id="comment" name="comment" class="span12" rows="5" aria-required="true"></textarea></p>',
        );
    comment_form( $comments_args );
?>

This is the result:

Now, I would like to add two CSS class (class="btn btn-primary") for submit button; how can I do that without using jQuery?

Note:

For the solution, please read comments about answer marked with green sign.