Oduwa, 19, and Ball, 20, represent manager Mark Warburton's eighth and ninth signings of the summer window.
Both Players are a product of the Tottenham youth system.
Ball spent the second half of last season on loan at Cambridge United, making 11 appearances, whilst Oduwa also appeared 11 times for Luton town.
Ball has represented England at Under-19 and Under-20 level, having previously represented Northern Ireland at younger age groups.
Oduwa has also played for England at youth level, representing his country at the Under-18 level.
Warburton will have both players available this Sunday as Rangers continue their Championship campaign away to Alloa.
Rangers have signed winger Nathan Oduwa and defensive-midfielder Dominic Ball on a season-long loan from Tottenham Hotspur.