Sky Sports News reported last week that Rangers were one of a number of clubs interested in Oduwa, a 19-year-old attacker highly rated by Spurs’ head coach Mauricio Pochettino.
It was understood a number of teams from the Dutch Eredivisie expressed an interest in taking the winger, including AZ Alkmaar, Roda JC and Feyenoord, while Coventry City were also keen on him.
But Rangers boss Mark Warburton has a strong relationship with Spurs, having successfully helped develop Alex Pritchard at Brentford last season, and both Oduwa and Ball will now continue their developments at Ibrox.
Rangers were invited to train at Hotspur Way several weeks ago and played a behind-close-doors friendly against a Tottenham XI in which Warburton had a look at several Spurs youth players.
Oduwa signed for Tottenham in 2012 and has two England U18 caps. He is yet to make a first-team appearance and spent time on loan at Luton last season.
Ball, 20, is a promising defensive midfielder who played 11 League Two games for Cambridge United last term.
He is an England U20 international, having represented Northern Ireland from U15 to U21 level, but, like Oduwa, he has not played a first-team game for Spurs.