The 25-year-old has joined the Ligue 1 outfit after just a year with the UAE outfit and is eager to seal a return to the Champions League
Barrada has agreed a switch to the Stade Velodrome after just a year with Al Jazira, signing a contract running until 2018 with the French side.
The 25-year-old, who was born in the French town of Provins, joined Al Jazira from Spanish side Getafe in July last year and went on to score 15 goals in the 2013-14 campaign.
He managed 10 goals in the Pro league from midfield, something new Marseille coach Marcelo Bielsa will hope he can continue in Ligue 1.
"I want to help Marseille to finish in the top three," the playmaker commented. "This is the place that this club deserves. I'm looking forward to playing, especially in the big games.
"My goal in the short-term is to regain my physical level before thinking about joining the team.
"This is a strong commitment to me, I see my long-term future with the club."
The midfielder becomes the third signing for Bielsa following in the footsteps of Romain Alessandrini and Michy Batshuayi and will look to go some way to fill the void of Mathieu Valbuena's departure.
Marseille were denied a winning start to their league campaign on Saturday as Bastia came from 3-1 down to record a 3-3 draw.