Meyler, 23, has been on loan at the KC Stadium from Sunderland for the past few weeks and signs a three-and-a-half-year deal. He is thought to be costing the Tigers £1.5 million.
Manchester United's Brady, 20, pens a contract of the same length following a successful loan spell. The fee for him is reported to be £2m.
The Republic of Ireland international has been in impressive form during his stay on Humberside with the left wing-back, scoring once in 12 games.