Abidal's departure comes less than 24 hours after coach Quique Setien was dismissed, with sources telling ESPN that Ronald Koeman will be named as his replacement imminently.
Ramon Planes, already at the club, will step into the role of technical secretary for now. He has been Abidal's No. 2 for the past two years.
"Barcelona and Abidal have reached an agreement for the ending of the contract that united the two parties," a short statement read.
"The club would publicly like to thank him for his professionalism, commitment, dedication and the close and positive nature of his relationship with all aspects of the Blaugrana family."
Abidal was only appointed to the role in 2018, but his position has grown increasingly insecure following a public spat with Lionel Messi in February.
The former France international, who played alongside Messi at Camp Nou, had been brought in to help bridge the gap between the boardroom and the dressing room.
However, cracks appeared when he suggested the players were to blame for Ernesto Valverde's sacking in January, as they had not been working hard enough.
Messi hit back in a post on social media, asking Abidal to name names and to take on some responsibility for his own decisions.
Results on the pitch and a first trophyless season since 2007-08 have served to further weaken his position, leading to his exit on Tuesday.
In his role as technical secretary, Abidal has been responsible for the makeup of the first-team squad and has also played a role in the hiring and firing of coaches.
Sources have told ESPN that he was one of the main advocates for Setien's appointment in January.
Abidal becomes the fourth person to leave the job under current president Josep Maria Bartomeu since 2015. Andoni Zubizarreta, Robert Fernandez and Pep Segura have all been fired from similar roles.
Meanwhile, Barca hope to announce Koeman as their new coach later on Tuesday, with big changes in playing personnel expected to follow in the coming weeks.
Bartomeu has resisted calls to resign. Instead, he has announced that the presidential elections, scheduled for next June, will instead take place in March. He cannot stand again.