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.
The midfielder becomes the third signing for Bielsa following in the footsteps of Romain Alessandrini and Michy Batshuayi.
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.
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