//first, get the image, and store it in your upload-directory:
$uploaddir = wp_upload_dir();
$uploadfile = $uploaddir['path'] . '/' . $filename;
$contents= file_get_contents('http://mydomain.com/folder/image.jpg');
$savefile = fopen($uploadfile, 'w');
fwrite($savefile, $contents);
fclose($savefile);
//after that, we can insert the image into the media library:
$wp_filetype = wp_check_filetype(basename($filename), null );
$attachment = array(
'post_mime_type' => $wp_filetype['type'],
'post_title' => $filename,
'post_content' => '',
'post_status' => 'inherit'
);
$attach_id = wp_insert_attachment( $attachment, $uploadfile );
$imagenew = get_post( $attach_id );
$fullsizepath = get_attached_file( $imagenew->ID );
$attach_data = wp_generate_attachment_metadata( $attach_id, $fullsizepath );
wp_update_attachment_metadata( $attach_id, $attach_data );