Cardiff have signed Reid from Bristol City on a four-year deal for a fee thought to be in the region of £10m.
"I'm delighted to be here and to be a Premier League player," Reid told the club's website.
"I want to show my high energy and work rate, as well as being creative and working for the team. I'm buzzing to get started."
Cardiff manager Neil Warnock said: "I've been after Bobby for a while now. I like the lad.
"By all accounts he's great around the dressing room. He can play in a number of positions and his best is yet to come.
"Players like Bobby and Josh Murphy are hungry, and that is what we need now. We're very happy to bring Bobby in."