The home secretary said CardinalHume had agreed the revised clause was the "best that can reasonably be achieved to reinforce the protection given by the Convention".
Head of the Catholic Church in England and Wales, Cardinal Basil Hume, had written to him supporting the redrafted clause, after having taken legal advice, said Mr Straw.
Last month, Cardinal Basil Hume, the leader of Catholics in England and Wales, was appointed to the Order of Merit, whose membership is chosen by the queen and limited to 24.