It calls for the couple to be blessed by God, and asks that "they may both live and grow in your love all their days".
Harry and the American former actress will be married by the Archbishop of Canterbury, the Most Revd Justin Welby in a religious service in St George's Chapel, Windsor Castle on May 19.
Ms Markle has only recently been welcomed into the Anglican faith.
She was both baptised and confirmed in a secret ceremony conducted in March by the Archbishop, who described the proceedings as "beautiful" and "very special".
The prayer reads:
God of love,
send your blessing upon Harry and Meghan,
and all who are joined in marriage,
that, rejoicing in your will
and continuing under your protection,
they may both live and grow in your love
all their days,
through Jesus Christ our Lord.
Amen
