The invitation to visit the capital city, Pyongyang, will be delivered by South Korean president Moon Jae-in who will be in the Vatican next week as part of a trip to Europe.
This is not the first time a pope has been invited to North Korea.
North Korea and the Vatican have no formal diplomatic relations.
"During the meeting with Pope Francis, [Mr Moon] will relay the message from chairman Kim Jong-un that he would ardently welcome the Pope if he visits Pyongyang," Mr Moon's spokesman, Kim Eui-kyeom, told reporters.
The invitation is the latest reconciliatory gesture from North Korea.