Bishop Griswold was educated at St Paul's School in Concord, New Hampshire and earned an AB 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). 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 ordained an episcopal priest in 1963 and then served at three parishes in Pennsylvania, including St Andrews 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.
Griswold was co-chair of the Anglican-Roman Catholic International Commission from 1998 to 2003, and 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 is known to have Anglo-Catholic tendencies.