Cardinals are the most senior members of the Roman Catholic church after the pope.
Cupich said in a statement that the pope's decision was "humbling and encouraging."
"The role of Cardinal brings new responsibilities, but with your prayers and help, we will continue the task we have begun of renewing the Church in the archdiocese and preparing it to thrive in the decades ahead," Cupich said.
The ceremony to elevate Cupich, where he will get the famed red hat worn by all cardinals, is set for Nov. 19. Archbishop William Tobin of Indianapolis and Bishop Kevin Farrell of Dallas were also named cardinals by Francis.
Despite his new role, Cupich will continue to serve as the leader of the 2.2 million Catholics in Cook and Lake counties, where he is leading an effort to overhaul the Archdiocese of Chicago's 351 parishes and 229 schools.
Pope Francis named Cupich to replace the ailing Cardinal Francis George as archbishop of Chicago in 2014 in his first major appointment in the American church.
In November 2015, Cupich announced that a newly created regional academy that will merge the schools of four Far Northwest Side Catholic churches would be named for Pope Francis, the first Chicago school to be named for the pontiff.
Cupich has said the merger is needed to preserve Catholic education at a time of declining enrollment and massive budget deficits and ensure the future of Catholic education in Chicago is "sustainable."
Like Francis, Cupich's tenure has been marked by efforts to welcome new members to the church rather than an emphasis on church doctrine.
Mayor Rahm Emanuel issued a statement of support Sunday, saying Cupich "has made a tremendous impact as a voice for the voiceless in the name of inclusion."
The archbishop has been "a light of inspiration for all of us, and a blessing to the City of Chicago," Emanuel added.
Cupich's predecessors were also named cardinals within two years of being named Chicago archbishop.
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