Free agent Padovani, 23, has signed a two-year contract with Pompey following his recent release from Monaco.
Pompey manager Guy Whittingham said: "We were alerted to Romain by Yassin (Moutaouakil's) agent. He came over to train with us and we could immediately see he was a decent player.
"He's hungry and that's the most important thing - he wants to come here and be successful. He's come through the Monaco system, so that tells you that he has to be a good player."
Moutaouakil has signed a new one-year deal with the club after making 19 appearances during the second half of the season.
The 26-year-old defender arrived from Hayes & Yeading in January and was a regular in Whittingham's starting line-up.
"Yassin got better as the season progressed and when he was playing at his best there weren't many who could get past him," Whittingham added.
Pompey signed striker Patrick Agyemang on a permanent basis on Wednesday following his loan spell with the club and defenders Sonny Bradley and Danny East arrived earlier on Thursday following their release from Hull.