There are at least seven versions of this carol, so this might not be the one with which you are familiar. More on that later.
This song began as a poem by Henry Wadsworth Longfellow (1807-1882), written on Christmas Eve in 1863. This was a dark period in Longfellow's life. His wife had died in a tragic fire two years earlier and his son had just been severely wounded while fighting in the American Civil War. The poem was entitled "Christmas Bells".
I heard the bells on Christmas Day
The version of this carol that appears in most hymnals is sung to a tune called "Waltham" by John Baptiste Calkin. Although his melody first appeared in 1848, the pairing of Longfellow's words to Calkin's music was first made in 1872. Other pairings have also been made over the years. One such was the tune "Mainzer", composed by Joseph Mainzer (1801-1851). Others include music by John Bishop (ca. 1665-1737), Alfred Herbert Brewer (1865-1928) and Isaac H. Meredith.
My favorite version is the one that opened with this page. It's a contemporary tune composed in 1956 by Johnny Marks, author of many holiday songs, most notably "Rudolph the Red-Nosed Reindeer". It's been performed in various arrangements by Kate Smith, Frank Sinatra, Harry Belafonte, Bing Crosby, Plácido Domingo and Sarah McLachlan. Folk-singer John Gorka performs his own version called "Chistmas Bells".
The background information given on this page came from The Hymns & Carols of Christmas and an article at the Military Order Of The Loyal Legion Of The United States website. Some of the information on these pages is contradictory and I've tried to sort it out.
I found many versions of the Calkin music but only one each of the Mainzer and Brewer MIDIs. You can find all of them at The Hymns & Carols of Christmas. I found only one rendition of the Marks version on the web (perhaps because of copyright concerns) although it was on several websites. I polished it up a bit for this presentation. You can find the original (and many other Christmas songs) at Mary's Christmas MIDIs.
I created by background from numerous graphics found by using Google Images on the terms 'steeple' and 'belfry'.