Jain will leave for Rome with Chief Minister Arvind Kejriwal on September 2 and return on September 5.
"The Lt Governor has cleared Jain's file to go to Vatican in Rome," sources said.
However, earlier in the day, Jain had alleged that the Lt Governor has not given his approval for the trip to attend Mother Teresa Sainthood ceremony in Vatican on September 4.
"Waiting for LG's approval (File on LG's table for Last 7 days), to attend Mother Teresa sainthood celebration in Vatican," Jain had tweeted in the afternoon.
Mother Teresa, winner of the Nobel Peace Prize, will be declared a saint by Pope Francis.
In July, Kejriwal had accepted the invitation of Missionaries of Charity to attend the event.