William Patterson Alexander was born in Paris, Kentucky on July 25, 1805. His father was James Alexander (1770–1821) and mother was Mary Rose Depuy (1765–1841). He attended Centre College in Danville, Kentucky and then Princeton Theological Seminary. He was a distant cousin of Archibald Alexander, the founder of the Presbyterian seminary. On October 25, 1831 he married Mary Ann McKinney who was born January 5, 1810 in Harrisburg, Pennsylvania. He was ordained October 13, 1831. They sailed on the Whaleship Averick, under Captain Swain, from New Bedford, Massachusetts, November 26, 1831, and arrived at Honolulu, May 17, 1832. Alexanders and the rest of the fifth company from the American Board of Commissioners for Foreign Missions arrived in April 1832 to the Hawaiian Islands.
They were sent on a scouting mission to the Marquesas Islands (at the time called "Washington Islands") with Reuben Tinker and Samuel Whitney. On July 2, 1833 they then traveled back to establish a Marquesas mission with Richard Armstrong, Benjamin W. Parker with their wives via Tahiti. However, they abandoned the Marquesas to European missionaries and arrived back in Honolulu on May 12, 1834.
The Alexanders were assigned to the mission at Waiʻoli 1834 until 1843. Looking for a drier climate, they were transferred to Lahainaluna School in 1843. After the departure of founder Lorrin Andrews and death of Sheldon Dibble, he became principal until 1856. He preferred to live at cooler, higher elevations, and often camped at what would become ʻUlupalakua Ranch. Although the American Board was withdrawing support, he continued to assist efforts such as the Kaʻahumanu Church in Wailuku, Hawaii from November 1856 until 1882. He and his wife traveled back to New Bedford by April 1858 on a fund-raising trip, and returned by December 1859. He helped unite Presbyterian and Congregational churches into the Hawaiian Evangelical Association. He died August 13, 1884 in Oakland, California and was buried in the Mountain View Cemetery.