1981 to 1989
Armour III earned his PGA Tour card at the end of 1981, but he only played in nine events in 1982 and was unable to retain full-time status. He spent time on European and Asian tours for several years before regaining a spot on the PGA Tour with an eighth-place finish in the 1987 Qualifying School. During this time, his most notable result was a win at the 1983 Mexican Open.
1990 to 1995
In 1990, Armour III posted his first PGA Tour win, taking the Phoenix Open by five strokes. He followed this up with a second-place finish in the Shearson Lehman Hutton Open three weeks later. Armour III was the first player to ever win consecutive Nationwide Tour events, taking the Miami Valley Open and Cleveland Open back-to-back in 1994. This helped him finish seventh on the money list at the end of the season and earn his PGA Tour card for 1995. In 1995, Armour III played in 30 PGA Tour events, making the cut in 16 of them.
1996 to 2000
Armour III had a dismal season in 1996, making only six cuts out of 22 events. He finished 11th at the year-end qualifying school to keep his spot on the tour. His performance in 1997 was steady, but unspectacular, making the cut in 18 of 30 events with no finish higher than 17th. In 1998, Armour III returned to the top 60 on the PGA Tour money list for the first time since 1990. His best finish of the year was a second-place in the Phoenix Open. He scored another second-place in 1999, losing the Touchstone Energy Tucson Open in a playoff. Armour III posted two top-10 finishes during 2000, taking fifth in the Nissan Open and 10th in the GTE Byron Nelson Challenge.
2001 to 2004
In 2001, Armour III finished 161st on the money list and had to qualify again for the PGA Tour at the year-end qualifying school. He posted three top-10 finishes during the 2002 season, but he was unable to finish high enough on the money list to keep his full-time status. Playing part-time in 2003, Armour III recorded his second career PGA Tour victory when he won the Valero Texas Open and set a PGA Tour record with his four-round score of 254. This win gave him a guaranteed two years of full-time status on the PGA tour. He would have retained his playing card in 2004 anyway, finishing 95th on the money list after taking ninth in the Honda Classic and second in the season-ending Chrysler Championship.
2005 to 2009
Armour III barely retained his playing card after the 2005 season. He made the cut in 10 of his last 12 starts to end the year ranked 122nd on the money list. In 2006, he was unable to crack the top 125 for the first time since 2002. His best result of the year was an 11th-place finish in the Zurich Classic. In 2007, Armour III placed fourth in the Shell Houston Open and fifth in the Turning Stone Resort Championship, ranking 98th on the money list at the end of the year. He earned over a million dollars for the first time during the 2008 season. He did not win any tournaments, but he placed in the top 10 a career-high five times. Through the first week of August, Armour III has played in 14 PGA Tour events in 2009, making the cut in nine of them.