Republic of Ireland international Brady, who has had three previous loan spells at the KC Stadium, has arrived on a permanent basis from Manchester United for a reported £2m fee.
Meanwhile, Meyler, who has also had a loan stint with the Tigers, has signed on from Sunderland.
"I'm delighted to announce I'v signed for Hull City on a three and half year deal.Looking forward to pushing for promotion starting Saturday," Meyler wrote on Twitter. "I'd like to thank everyone at SAFC for everything, also the amazing fans for there support over the past 4 years. Special club."
Both players have agreed deals until the summer of 2016.