Young, the son of Detroit's first black mayor Coleman A. Young, conceded the race as Duggan held a commanding lead with nearly all of the precincts reporting.
The victory allows Duggan to continue efforts to remove blight and bring improvements to city neighborhoods.
In the nonpartisan August primary, Duggan got more than 67 percent of the vote to Coleman Young II's nearly 27 percent. Duggan received endorsements from prominent labor groups and clergy, and even the influential Black Slate that helped get Young's father get elected in 1973.
Coleman A. Young, who first took office in 1974, served 20 years as mayor. He decided not to seek re-election after 1993. He died in 1997.
Duggan was elected the first white mayor in the city since 1973. Detroit is more than 80 percent black.
"I hope that this is the year where we put 'us versus them politics' behind us forever, because we believe in one Detroit for all of us," Duggan told his supporters Tuesday night. His supporters then began to chant: "One Detroit. One Detroit."
Duggan initially took office months after a state-appointed manager in 2013 filed for Detroit's historic bankruptcy. Duggan had limited power over city finances and other operations in his first year in office, but he and the City Council eventually regained control after Detroit's December 2014 bankruptcy exit.
The bankruptcy allowed Detroit to restructure or shed billions of dollars in debt.
Under an aggressive blight removal plan and using primarily federal funds, more than 10,000 vacant houses have been torn down over the past four years. Duggan also has worked with banks and foundations on home-buying and renovation programs to improve Detroit neighborhoods.
Chauncey Sanders, 47, said he sees the physical improvements in Detroit and better city services. He voted for Duggan.
"The police are showing up when I call them. Streets are getting swept. I haven't seen that since Coleman (A.) Young," said Sanders, a barber, who added that he didn't know much about Coleman Young II and that race shouldn't be a factor in who runs Detroit.
"I ain't looking at color either," he said. "As long as he is doing a good a job."
But Young has criticized Duggan, saying some of Detroit's poorest neighborhoods have yet to get better.
Young had been a state representative and was elected to the Michigan Senate in 2010. He ran unsuccessfully in a 2009 special mayoral primary to complete the second term of convicted ex-Mayor Kwame Kilpatrick. Kilpatrick served as mayor from 2002 to 2008. He resigned in disgrace as part of a plea deal in separate perjury and assault cases.
Young told his supporters during his concession speech Tuesday night that the campaign against Duggan was hard-fought.
"And even though ... we came up short, this is just the beginning," Young said. "The struggle continues, and the revolution moves on."