No financial details were disclosed but the Premier League club said they had broken their previous record fee of 10 million pounds ($13.08 million) for England international Mason.
Injuries restricted him to eight league appearances for Spurs last season and he has not featured under Mauricio Pochettino in the new campaign.
"I'm delighted and excited to be here," the 25-year-old told the club website (www.hullcitytigers.com). "I can't wait to get started and I see this as a massive opportunity."
Keane worked with Mike Phelan when the Hull manager was Alex Ferguson's assistant at United.
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The 23-year-old has also had loan spells at Wigan Athletic, Queens Park Rangers and Sheffield Wednesday.
"It's hopefully going to be a good ride and I can't wait to get started," said United squad player Keane.
Hull travel to Burnley for their next league fixture on Sept. 10.
(Reporting by Nivedita Shankar and Mark Greaves, editing by Ed Osmond)
