Andreazzoli has been named interim coach after the sacking of Zdenek Zeman.
"I consider it a very intelligent choice. He knows Roma well and has lived in the city for eight years," Spalletti told Sky Sport Italia.
"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."