The Bishop, the first African-American to be elected into the prestigious role, will travel from his home in Chicago Illinois, to Windsor to take part in the service.
The Most Revd. and Rt. Hon. Justin Welby, Archbishop of Canterbury, will officiate as the couple make their marriage vows.
Prince Harry and Ms Markle have not yet met the bishop and have no previous relationship with him, but choose him to deliver their address after discussions with Archbishop Welby.
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Bishop Curry said: “The love that has brought and will bind Prince Harry and Ms. Meghan Markle together has its source and origin in God, and is the key to life and happiness. And so we celebrate and pray for them today.”
A spokesman for Kensington Palace said: “The couple and the Archbishop discussed a number of possibilities for a preacher.
“Whilst Bishop Curry is not personally known to the couple, it was felt that given the fact that he the Presiding Bishop of the Episcopal Church (Anglican Church in the US) as well as a wonderful speaker and preacher, it would be highly appropriate for him to be invited to speak.”
The Episcopal Church is an offshoot of the Church of England in the US and forms part of the broader Anglican Communion worldwide.
Ms Markle was baptised by the Most Rev Justin Welby ahead of her wedding to the prince, whose grandmother, the Queen, is head of the Anglican Church.
Writing on Twitter, Archbishop Welby said: “I’m thrilled that Prince Harry and Meghan Markle have asked Bishop Michael Curry to preach at their wedding.
” @PB_Curry is a brilliant pastor, stunning preacher and someone with a great gift for sharing the good news of Jesus Christ.
“Marriage is a special and joyous commitment – please join me in praying for God’s blessing for the Royal couple on their wedding day, and for the whole of their lives together.”