The Enfield-born striker, 20 - no relation to the Manchester City and England frontman Raheem - will go straight into the squad ahead of Saturday's League One home game with Fleetwood Town.
Sterling, who has represented England at under-18 and under-17 level, joined Spurs from neighbours Leyton Orient in July 2015
During his development, the speedy striker figured prominently for Spurs in the Premier League 2, FA Youth Cup and UEFA Youth League.
Sterling has played four games in EFL Trophy for Spurs over the past two seasons and made his competitive senior debut in December 2017 when he came on as a late substitute for Dele Alli in Spurs' final Champions League group game against APOEL Nicosia at Wembley Stadium.
He also featured for the Londoners in their FA Cup exit at Crystal Palace in January before being loaned out to Sunderland in the second half of last season, where he made eight appearances.
Sterling scored his first senior goal in a 3–0 away win against Accrington Stanley in April.
On the signing, Rovers boss Darren Moore said: “Kazaiah is a forward who is really highly-rated at Spurs, they see him as a first-team player for them very soon and he just needs more experience at senior level.
“He has an excellent record at under-23 level, has been recognised internationally and has scored when he has stepped up to senior level - I am really excited to add him to my squad.
"We have had to be patient on this signing because his parent club see him as having a big role for them, we respect that but believe he can make a real impact for us this coming season."