The left-sided centre back is available on a free transfer after being released by Motherwell, who are in administration.
City boss Jan Molby said of his first permanent signing: "Greg is the type of centre-half that I've been after and it's great that he wants to join Hull City.
"He's powerful, is good in the air, is an organiser and a leader and has captained Motherwell.
"Greg's also the right age and I believe that your centre-halves are the heartbeat of the side."
City have already signed Stuart Green on loan for the season from Newcastle, and Richie Appleby's move will go through when his contract at Kidderminster expires on 30th June.
Rumours that City are set to sign Tranmere's Wayne Allison are thought to be inaccurate, but Jan Molby has said that City are still looking for a big centre forward.
"We've talked to a number of forwards but there's no one yet I feel I really want," he said.
"There's no point diving in now and finding someone much better becomes available in three or four weeks.
"I can appreciate the fans are desperate for something to happen but patience is the key."
Meanwhile the Dane is leaving for Japan and South Korea over the next few days for World Cup media work.