Scores of priests, nuns, deacons and others from the 225,000-member diocese attended the installation Mass lasting more than two hours at Sts. Peter and Paul Cathedral in Indianapolis.
"I come to you as your chief pastor, not your only pastor," the 60-year-old Detroit native told them.
More than 1,100 people, including other bishops and clergy of other faiths attended the Mass.
At the time of his Oct. 18 appointment, the Redemptorist bishop was a top Holy See official for religious orders who tried to resolve tense relations between the Vatican and American nuns.
The installation occurred on the feast day of St. Francis Xavier, the principal patron of the archdiocese covering 39 counties across central and southern Indiana. The colorful events began with Tobin walking up the outside steps of the cathedral and knocking on the doors to announce his arrival and lay claim to the church in Indianapolis.
After the start of the Mass, Archbishop Carlo Maria Vigano, the apostolic nuncio and highest-ranking Vatican official to the U.S., read the letter from the pope announcing Tobin's appointment.
Also among those attending were Archbishop Daniel Buechlein, who retired from the archdiocese last year, and Auxiliary Bishop Christopher Coyne, who had been acting administrator after Buechlein stepped down.