Andreazzoli was the assistant to the Italian when he was in charge of the Roman outfit between 2005 and 2009.
"I consider it a very intelligent choice," Spalletti told Sky Sport Italia. "He knows Roma well and has lived in the city for eight years.
"He has the spirit of a Romanista and by sitting in the background over all these years he was able to gain experience, forming his own ideas. He can be the right man for the job.
"When I went to Zenit St. Petersburg, he decided to remain with Roma. He deserves this chance and the time to work without having to hand over to anyone else. He is not a caretaker.
"Andreazzoli knows the 4-2-3-1 system very well and looking at the current squad it could be used again. He deserves Roma's faith and the club knows that the players have faith in him."
Roma are currently eighth in Serie A.