World Cup and European Championship winner Villa, 30, suffered the injury during the 4-0 semi-final win over Al-Sadd of Qatar in Japan.
After undergoing successful surgery, Spain’s all-time record goal-scorer was ruled out for around five months, leaving him in a race against time to be fit for Euro 2012, which starts in June.
"I am very positive, going through the final phase now, thank God, working very hard every day since it happened," Villa said at a Spanish FA event.
"I can see light at the end of the tunnel and I am eager to start enjoying football again from the inside."
Villa scored 32 goals in 76 games since joining Barca from Valencia at the start of last season.
He has 51 goals in 81 games for the Spain national team, seven goals ahead of second-placed Raul, who has not played for his country since 2006.