Greenlee County was named after Mason Greenlee, an early-day mining man. He was born in Virginia and came to Denver, Colorado after the close of the Civil War when that city was only a mining camp. He soon became interested in mining and organized a company, which prospected the Big Horn country. He located several gold claims in Colorado, one of these was the "Wheel of Fortune", which made him quite wealthy.

Greenlee was described as a tall man, quite thin and tireless. He was fearless, living by himself when the Indians were on the warpath. Although his hearing was impaired, he loved to talk and joke. He seemed to have been one of those fortunate people who was well like by all who knew him.

In 1871 J.H. Holbrook organized a party in Pueblo, Colorado to prospect the Gila River Valley. Greenlee joined the party, which consisted of twenty-one men, many of whom were old soldiers. Soon they were near Clifton and Morenci. (Neither of those towns existed then.) They stayed in the vicinity most of the winter but returned to Colorado when the Indians became troublesome. Greenlee was very impressed with the gold prospects which he saw and was determined to go back. He sold his valuable mine, "The Wheel of Fortune" and returned to Clifton in 1878. With him came Lloyd Tevis who was Greenlee's partner until his death. With several other miners they established the Greenlee Gold Mountain Mining District, which was located on the San Francisco River several miles above Clifton.

The remainder of Greenlee's life follows a tragic pattern common among the early day prospectors. His efforts to locate a rich strike slowly ate up the sizable fortune which Greenlee had brought with him from Colorado. During the nineties Greenlee and Tevis consolidated their holdings with Hank Dorsey and Albert Williams. They believed they had a rich strike but the gold was never found.

In 1898 Greenlee's health began to fail due to the hard work he had done. During the winter of 1902 and 1903 he spent in Clifton, in the home of an old friend Ike Stevens. Greenlee died April 10, 1903 after being ill for three weeks following a collapse. He was buried in an unmarked grave at public expense. The citizens honored the memory of Greenlee by erecting a large monument at his grave.

It is very unlikely that the name of Greenlee would have been adopted as the name of the county. The Arizona Copper Company wished to name the county after Mr. Colquhoun, who was head of that company. Detroit Copper Company wished to name it to honor Dr. Douglas who was in charge of that company. The proposal caused the leaders to give up their own proposed name of Colquhoun and substitute Lincoln instead. A bill was passed in the house with an amendment to change the name from Lincoln to Greenlee to delay final passage of this bill. Greenlee had died a few years previously and was well remembered at that time.