The Vatican said the pope wanted to show his appreciation for the warmth he was shown when he visited the United States, the BBC reported.
"It's a great honor," Bush told Benedict, who met the president at his car, ANSA, the Italian news agency, reported. First lady Laura Bush also spoke with the pontiff, thanking him for the invitation.
Bush and the pope agree on issues such as abortion, stem cell research and humanitarian aid to Africa. However, the two disagree on Iran -- the Vatican has open diplomatic relations with Tehran unlike the United States.
Bush flew to Europe this week to attend the EU summit in Slovenia and to visit several countries, likely for the last time as president. Bush's next stop is Paris, where he will meet with French President Nicolas Sarkozy.
2014: The Year in Music [PHOTOS]