The son of Syrian immigrants, Atiyeh grew up in Portland, attending Holladay Grade School and Washington High School. He spent two years at the University of Oregon in Eugene, where he played guard for the Oregon Ducks football program and became a regional leader in the Boy Scouts of America. When his father died Atiyeh dropped out of college and took over his family's rug and carpet business, Atiyeh Brothers.
Atiyeh served as a member of the Oregon House of Representatives from 1959 to 1964 and in the Oregon State Senate from 1965 to 1978. In 1974, he ran for governor and lost to Democrat Robert W. Straub. After defeating former governor Tom McCall in the primary Atiyeh ran against Straub again in the 1978 election, but won this time with 55 percent of the vote. In 1982, he won re-election to a second four-year term, winning by the largest margin in 32 years for a gubernatorial election in Oregon.
As governor, Atiyeh established new public safety programs for Oregon's traditional fishing and lumber trades. He provided incentives to bring new industries to the state to diversify the economy, including the opening of a trade office in Tokyo, Japan, Oregon's first overseas trade office. He launched a worldwide tourism initiative and worked towards the designation of the Columbia River Gorge as a national scenic preservation area.
Atiyeh helped to establish a statewide food bank, which was the nation's first. He also worked to raise awareness of the dangers of drunk driving and signed new laws against the practice. He chaired the Republican Governors Association and was the Republican National Convention's floor leader for President Ronald Reagan in 1984.
Atiyeh had a long relationship with Forest Grove-based Pacific University, serving as a trustee and trustee emeritus and accepting an honorary doctorate from the university in 1996. He donated a trove of his memorabilia to the university library in 2011.
After leaving office, Atiyeh became an international trade consultant. On August 31, 2005, he underwent quadruple bypass surgery; he drove himself to St. Vincent Medical Center after suffering chest pains. Atiyeh was noted for his fiscal conservatism; his spokesman noted that he had stopped on his way to the hospital to fill his car with gas, having observed the sharply rising prices. In the weeks following the surgery, Atiyeh was readmitted to the hospital for several brief stays after suffering shortness of breath and pain in his arms.
In 2006, Atiyeh co-chaired the "Yes on 49" campaign, supporting Ballot Measure 49, along with Democratic former governor Barbara Roberts, former and future governor John Kitzhaber, and then-governor Ted Kulongoski. He solicited a $100,000 donation to the campaign from Phil Knight, CEO of Nike.
On July 20, 2014, Atiyeh died of renal failure at Providence St. Vincent Medical Center in Portland, which was contracted after a fall he sustained at his home on July 5. He was 91.
Atiyeh lived in Portland with his wife, Dolores (née Hewitt), whom he married on July 5, 1944. Atiyeh and his wife had two children, Tom and Suzanne. Dolores died on August 29, 2016, in Portland at the age of 92.