The Kent-born winger made his debut for the club at the age of 16 in October 2001 in a 1-0 home defeat against West Bromwich Albion.
He made his first start, aged 17, against Wolverhampton Wanderers and scored after just one minute on the pitch and also played a part in the side which won promotion to the Premier League via the play-offs in 2003-04.
In 2005 he joined Tottenham, during which time he also spent loan-spells away at Portsmouth and Fulham before joining Aston Villa in January 2008.
He also had a recent spell at fellow Championship side Cardiff City in 2008.
Routledge will wear the number seven shirt and is set to be unveiled before Saturday's FA Cup tie against Burnley.
Meanwhile, Borrowdale joined the R's on loan in late November but has failed to feature for the first team.
He joined Coventry City in July 2007 from Crystal Palace and also spent time on loan at Colchester earlier this season.
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