The 28-year-old full-back joins the Ligue 1 club on a three-year contract and will wear the No.2 shirt.
"I'm very happy to join FC Nantes," Fabio told the club's official website.
"I'm really looking forward to training and being ready to help my team-mates.
"I already know them a bit because I have seen matches on TV, I know some players and to be honest, I am very enthusiastic!"
After starting his career at Fluminense, Fabio made the move to Old Trafford in 2008-09 along with brother Rafael under Alex Ferguson but rarely featured for the first team.
A loan to Queens Park Rangers came 2012-13, as he made 21 appearances and 13 starts for the London club, who finished bottom of the league and were relegated.
The defender made 13 starts for Cardiff down the stretch but the club were relegated to the Championship at the end of that season.
Fabio went on to be a regular in the Bluebirds' back four in the Championship until he secured a move back to the Premier League with Middlesbrough in 2016.
The defender made 24 appearances in the Premier League that season, with 21 starts. However, another relegation followed, with Fabio playing 24 games last season for Boro in the Championship, starting 18 of them.
After 11 years in the UK I cannot wait to start this new challenge at @FCNantes I feel honoured to join this famous club and I look forward to helping Nantes achieve its goals. #AllezFCNantes Thanks to the team @KeySportsMGMT pic.twitter.com/FeIL2k7uNB — Fabio Da Silva (@Ofabio3) July 18, 2018
The two-time Brazil international will now get another shot at top-flight football after signing a three-year contract at Nantes.
Nantes finished ninth in Ligue 1 last season, 41 points behind winners Paris Saint-Germain.