Ivan Rakitic had the armband last season, but the Croatian moved on to Barcelona this summer.
As a result, Federico Fazio was appointed as the new skipper, but the defender also sought pastures new – joining Tottenham Hotspur.
Coke was appointed skipper following the Argentine's departure and he has vowed to wear the armband with pride.
"I've been here a while now but it was still a touching moment. I'll keep doing my best for Sevilla even if I don't have the armband or I'm not in the lineup," Inside Spanish Football quotes Coke as saying.
"I don't think the responsibility weighs on me – I have to be a little more attentive for situations, like talking to the referee.
"It's a matter of pride and I feel privileged to wear the armband for a club with so much history, and after being here for a while now, it feels like my own."
Sevilla currently sit third in La Liga.