Born in London, England, during his teenage years Maxwell was schooled at Stanborough College upon the insistence of his mother. At age 16, Maxwell worked for a period as a literature evangelist, before becoming a copyreader at Stanborough Press. On May 3, 1917, Maxwell married a proofreader at the office, Rachel Elizabeth Joyce, with whom he had four sons and two daughters.
Maxwell began writing articles for The Present Truth magazine. During this period he also had articles published in the Signs of the Times. In 1920, Maxwell became editor of the Present Truth and until 1927 was also manager and treasurer of the Stanborough Press, pastor of a nearby church, official Adventist spokesman for church-state affairs in Britain, and editor, in addition to Present Truth, of a health journal.
He wrote a total of 112 books during his lifetime, and is known affectionately by Adventists around the world as "Uncle Arthur." His most notable publications include the Bedtime Stories and The Bible Story volume sets. The simple stories are morality tales that illustrate values such as honesty, diligence, obedience, and selflessness. Volume 1 of The Bible Story, which tells the story of Genesis, upholds the historicity of the Bible account, including the creation of life on earth during a six day creation. This book was found in many doctors' offices in the United States during much of the 20th century.
Arthur's children Maureen, Graham, Lawrence and Mervyn have also done their own writing.
In 2006, Maxwell's book Secret of the Cave was turned into a feature film of the same name by students and faculty at Southern Adventist University. The direct to DVD film won the 2006 Crystal Heart Award from the Heartland Film Festival in Indianapolis, Indiana, and has received Dove Family-Approved seal