Greer told BBC Sussex: "It's a big honour for me and hopefully I can do a good job. When the manager asked me I was delighted to take it on board.
"I'll try and lead by example. I'm quite vocal on the park and in training and hopefully it rubs off on people."
He added: "I give my all every game as a player and in my opinion you can't do more than that."
Greer captained Swindon in League One last year but says that gaining the armband was not on his mind when he joined the Seagulls.
"When the opportunity came up to come here it was just footballing reasons," he said.
"I never even spoke about the captaincy and didn't expect to be named captain when I came here."
Brighton start the season away to Swindon on Saturday, but Greer will miss the first two games of the campaign through suspension.
Source: BBC Sport