Hartlepool have announced they will not sign convicted rapist Ched Evans after boss Ronnie Moore expressed an interest.
Arsenal manager Arsene Wenger insists he will only spend money in January on the right player.
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.