The jersey became vacant following Lionel Messi's shock departure to Paris Saint-Germain this summer, and 18-year-old Fati was entrusted to take the reins.
The forward has missed the last 10 months of action with a knee injury, marking his return in Sunday's 3-0 win over Levante with a well-taken goal.
"I did not imagine a return like this," Fati said, via Marca. "I am happy for the victory, there is still a long way to go.
"Thanks to the doctors and physios who have been with me. I am happy to help the team and for my family who have been suffering these months. I am very grateful to all."
When asked about inheriting the number 10 shirt, Fati added: "It is not a pressure. I am proud to wear the number 10 after Leo. I am happy with the club and captains for the opportunity."
Sunday's victory ended a run of three games without a win for Barcelona, who have struggled after a summer of upheaval. Pressure is on Ronald Koeman to turn results around, though 90min understands Barça are already planning on life after the Dutchman.
Fati outlined Barcelona's lofty objectives for the new season despite their tough start, adding: "We are Barça. We are going for La Liga, the Champions League and all competitions. We are Barça and we have to fight and work."
Barcelona's win over Levante leaves them sixth in La Liga, five points adrift of table-toppers Real Madrid, but with a game in hand. They face Benfica in the Champions League group stage on Wednesday, looking to bounce back after losing to Bayern Munich on the opening matchday.