Asahel Wheeler was born on 1 March 1741, in Sudbury, Massachusetts,  the son of Lieutenant Elisha Wheeler, an officer of the Sudbury Militia and veteran of the French and Indian War, and Mary Loring, the daughter of the Reverend Israel Loring.  

He is recorded in the muster roll of the Sudbury Militia as a Second Lieutenant in the West Minute Company under Captain John Nixon. On the morning of the Lexington Alarm in 1775, he - along with his five brothers, his father Elisha, father-in-law Captain Aaron Haynes, and many other extended relations - marched north with the Sudbury Militia to neighboring Concord as part of Colonel Abijah Pierce’s Regiment, where he participated in the battle at Concord’s North Bridge. A minute man by training, he was among the many who chased the surviving British regulars back to Boston. He afterward enlisted in the Continental Army, being commissioned as Captain, where he commanded a Sudbury company under Colonel Ephraim Doolittle at Bunker Hill. He later served as Captain in Colonel Jonathan Read’s Massachusetts Regiment in 1775-1776 and in Colonel Ezekiel Howe’s Regiment, which was subsequently used to reinforce the Continental Army. He also saw service at Ticonderoga, the Canadian Campaign in Quebec, and again at Saratoga. At the war's end, he returned to Sudbury, where he was recorded in the 1800 Census, and his will was filed in 1810. 

The Patriot died on 31 October 1820 at the age of 82 and was buried in Sudbury’s Revolutionary War Cemetery. 

Of note is also his ancestry as the second Great-Grandson of Resolved White, who came to Massachusetts on the Mayflower at the age of five with his parents, William White and Susannah (Jackson) White, in 1620.