The right-back joined the club from Shildon in June 2018, and has amassed a total of 92 appearances in the yellow and black.
Groves, who has plied his trade in League Two for Darlington, will be joined by newly named vice-captain, Darren Lough.
"It's an absolute pleasure," said the full-back.
"With Louis [Storey] leaving, someone would always have to step in, but I think we have a lot of leaders on the pitch.
"I've been here for nearly four years now, so I can't wait to put on the armband."
Click here to watch Groves' full interview upon being appointed club captain.