Gomez and Mahony will preside jointly over symbolic ceremonies of transition at downtown's Cathedral of Our Lady of the Angels at 10 a.m. and 12:30 p.m.
Sunday is Mahony's 75th birthday, the traditional time for a Catholic archbishop to retire.
His successor is the Mexico-born Gomez, 58, who became an American citizen while serving in Texas as a priest for the conservative Catholic organization Opus Dei. He becomes the first archbishop of Mexican descent to head a North American archdiocese.
In the ceremony following Mahony's final homily as archbishop, the cardinal's coat of arms will be removed from above the archbishop's chair and Gomez's will be installed in its place.
Mahony will then escort the new leader to the throne and give him his pastoral staff, the symbol of his role as chief shepherd of more than 5 million Catholics -- of which about 70 percent are Latino -- in the archdiocese's coverage area of Los Angeles, Ventura and Santa Barbara.
Gomez will lead the remainder of the morning's Mass, which will be repeated at 12:30 p.m. in Spanish.
Mahony was appointed bishop of Stockton in 1980 and archbishop of Los Angeles in 1985, becoming the first native Angeleno to hold the office. He was elevated to cardinal by Pope John Paul II on June 28, 1991.
After the Cathedral of Saint Vibiana was damaged in the 1994 Northridge Earthquake, Mahony spearheaded the construction of Our Lady of the Angels, which was dedicated on Sept. 2, 2002.
Gomez was born in Monterrey, Mexico, and studied accounting there before receiving a doctorate in theology at the University of Navarra in Spain.
He was the priest in residence at Our Lady of Grace Catholic Church in San Antonio from 1987 to 1999. As the archbishop in San Antonio, Gomez helped establish the Hispanic Seminary of Our Lady of Guadalupe in Mexico City, which opened in 2000.
In 2001, he was ordained an auxiliary bishop for the Archdiocese of Denver. He also organized Denver's Centro San Juan Diego for Family and Pastoral Care, a place for formation of lay leaders and a base to provide welcoming services to immigrants.
Although he championed social justice and Latino immigrant rights, Mahony's legacy is tarnished by the sexual abuse scandal involving more than 500 victims and a record $660 million settlement. He also was accused of failing to report abusive priests to civil authorities and keeping them employed in parishes without informing parishioners.