Inter Milan director-general Marco Fassone has insisted that coach Walter Mazzarri has faith in Fredy Guarin.
Free agent James McFadden is waiting on the 'right' offer before agreeing a return to competitive action.
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.