'I would have like to have stayed and played on at Barcelona but the club saw it differently and I have to respect their decision,' an emotional Abidal said.
Abidal, who won 15 trophies in his six seasons in Catalonia, appeared in four La Liga matches during the end of the season, starting two.
'I hope to return because it is a club (that is) very special to me,' Abidal added.
'It's a very difficult day for me,' he said via Barcelona's official Twitter account.
'I have played for Barca for six years and it's been the biggest experience of my life. I understand and respect the decision of the club.
'I'm going, but I'll be sure to return. I want to thank all the fans of the club who have supported me and have been looking after me.
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'The team is my second family. We have gone through a lot together and I'll remember this forever.'
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His career at the Nou Camp has been littered with trophies, which includes four domestic league successes, three Copa del Rey triumphs and two Champions League winners' medals.
However, his health problems have seen him play an increasingly limited role in the last two years although his resilience in spite of these setbacks has won the hearts of football fans all over the world.
While Barcelona were unable to give him a new playing deal, club president Sandro Rosell has offered Abidal a technical director role.
'Abidal has won our heart and has demonstrated such important things about life,' he said.
'The doors are open for Abidal to be the technical director of all of our football academies.
'Abidal has the ideal profile to be the director of all of our football academies.'