The cross was accompanied to its new site Saturday by the Rev. Brian Jordan of St. Peter's Church, who ministered to first responders and survivors of the Sept. 11, 2001 attack on the United States, the New York Post reported.
He was joined in the ceremony by former New York Mayor Rudy Giuliani and family members of those who died.
"After a 10-year journey of faith, the World Trade Center Cross has finally found its home," Jordan said. "I am grateful to the leadership of the Memorial Museum for their sensitivity, compassion and professionalism. I urge all those who believe in the consolation and power of the cross to visit it in its future home in the Memorial Museum."
The cross was made from two metal beams that remained standing after the twin towers collapsed.
The cross is "an important part of our commitment to bring back the authentic physical reminders that tell the history of 9/11 in a way nothing else could," said Joe Daniels, president of the memorial. "Its return is a symbol of the progress on the Memorial & Museum that we feel rather than see, reminding us that commemoration is at the heart of our mission."
The memorial will be dedicated on Sept. 11, the 10th anniversary of the attacks. A museum will be opened at the site in 2012.