Griswold was educated at St Paul's School in Concord, New Hampshire and earned an B.A. in English literature from Harvard College (1959). He attended the General Theological Seminary and earned his BA in theology and MA from Oriel College, Oxford University (1962, 1966).
Griswold was ordained an Episcopal priest in 1963 and then served at three parishes in Pennsylvania, including St Andrew's Church in Yardley, Pennsylvania, and St Martin-in-the-Fields in Chestnut Hill, Philadelphia, Pennsylvania, from 1976 until his nomination as Bishop of Chicago. Griswold served as Bishop of Chicago from 1987 until he became presiding bishop in 1997. He has received honorary degrees from the General Theological Seminary, Seabury-Western Theological Seminary, Nashotah House, Sewanee, The University of the South and Berkeley Divinity School.
Griswold was co-chair of the Anglican-Roman Catholic International Commission from 1998 to 2003. He was a member of the standing committee for the 1998 Lambeth Conference. He has also served on diocesan, national and international committees for liturgy, worship and ecumenism. He is also a member of the Fellowship of the Society of St. John the Evangelist and broadly identifies himself as being in Anglo-Catholic tradition.  He is interested in interfaith dialogue and currently sits on the Board of World Religious Leaders for the Elijah Interfaith Institute. 
His term as presiding bishop ended on November 1, 2006. He was succeeded by the Most Rev. Katharine Jefferts Schori, the first woman primate in the Anglican Communion.
He and his wife Phoebe Griswold live in Philadelphia, Pennsylvania. They have two daughters, Eliza Griswold, an author and journalist, and Hannah, who with her husband Gavin McFarland have given them two granddaughters.
- The Most Revd John M. Allin, 23rd Presiding Bishop
- The Rt Revd Francis G. Burrill, 8th Bishop of Chicago
- The Rt Revd James W. Montgomery, 9th Bishop of Chicago
- Prichard, Robert W.; Pub Co, Morehouse (1999). A history of the Episcopal Church. Harrisburg, PA: Morehouse Pub. p. 343. ISBN 0-8192-1828-6.
- Webber, Christopher (2004). Give us grace: an anthology of Anglican prayers. Harrisburg, PA: Morehouse Pub. p. 445. ISBN 0-8192-1962-2.
- Photographs of at Saint Clement's Church
- The Elijah Interfaith Institute - Christian Members of the Board of World Religious Leaders
- episcopalchurch.org List of Presiding Bishops
|Episcopal Church (USA) titles|
James W. Montgomery
|10th Bishop of Chicago
William D. Persell
Edmond Lee Browning
|25th Presiding Bishop
January 1, 1998 – November 1, 2006
Katharine Jefferts Schori