Koeman's 14-month reign came to an end following Barca's 1-0 defeat to Rayo Vallecano on October 27, with the Dutch boss failing to convince, goal.com reported.
Barca have now turned to another club legend in an effort to steady their ship, with World Cup winner Xavi completing an emotional homecoming as he takes over the reins from interim boss Sergi Barjuan.
Qatari club Al Sadd said in an official statement: "Club administration have approved the transfer of Xavi to Barcelona after the payment of the clause stipulated in his contract. Xavi is considered an important part of our history and we wish him every success in the future."
Xavi is one of the most decorated players in Barca's history, having won 25 trophies at Camp Nou between 1997 and 2015 including eight Liga titles and the Champions League.
The Spaniard made 767 appearances for the club, a record bettered only by Lionel Messi, and also contributed 85 goals and 185 assists.
Xavi left Barca for Al Sadd in 2015 and retired four years later before becoming the Qatari side's permanent manager, and delivered the league title in his second season at the helm.
Al Sadd won five more trophies under the 41-year-old, who has now decided the time is right to head back to Camp Nou having rejected previous offers from Barca due to a lack of coaching experience. He had made it clear to reporters he wanted to head home when fresh rumours surfaced.
He said: "I really want to go home. I hope it happens. I have a contract and now the clubs have to negotiate. They already know my position."
Xavi has got his wish, after Barca officials flew to Qatar to thrash out a deal with Al Sadd and their top coaching target before an agreement was finalised.
Xavi will be a popular appointment among the Blaugrana faithful, but it will take a monumental effort for him to turn the team's fortunes around following their poor start to the 2021-22 campaign.
Barca have already lost three Liga games including a painful Clasico defeat at home to Real Madrid, with Koeman having ultimately failed to find the right balance in the squad after Messi, Antoine Griezmann and a number of other key players departed in the summer.
New signings Memphis Depay and Eric Garcia have yet to reach their best levels while Sergio Aguero is ruled out long term with health problems, and the Catalan club sit ninth in La Liga while also finding themselves in danger of being dumped out of the Champions League at the group stage.
Xavi will hope to hit the ground running, with Barca travelling to Celta Vigo today before entering another international break that will give a new boss time to find his feet in familiar surroundings.