New Tranmere boss Micky Adams has bolstered the clubs attacking options with Cardiff's Danny Johnson on a one-month loan.
Full-back Maynor Figueroa has returned to Wigan on a one-month loan deal from Hull.
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.
Manchester United's Brady, 20, pens a contract of the same length following a successful loan spell.
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.