Chiesa will serve until a new senator is elected in a special election Oct. 16.
Christie said he will file the necessary paperwork and Chiesa will be sworn in Monday, The Washington Post reported.
"There are very few people in my life that I know better than Jeff," Christie said. "You won't find anybody, I think, who will have something bad to say about Jeff."
Chiesa, a Republican, served with Christie when the governor was a U.S. attorney and led Christie's transition team when he won the 2009 governor's race.
Chiesa was appointed attorney general in January 2012.
Chiesa said he won't seek the seat in the special election.
Asked about his view on immigration -- a key issue he likely vote on while in Washington -- Chiesa said he is a border-security-first Republican, the Post said.
"I think the first thing we have to do is make sure the borders are secure," he said. "From there, these issues are new to me."
Lautenberg, a Democrat and the oldest member of the U.S. Senate, died Monday of viral pneumonia. He was 89.