He told the club's official website: "I've had a couple of good years with Burnley but now I'm really looking forward to my time at Forest."
The Welsh international hasn't trained for four weeks so is behind on fitness compared to the rest of the squad.
He could make the substitutes bench for Saturday's game against Norwich but a realistic target for his first competitive start could, ironically, be against his former club at Turf Moor on Tuesday 16 September.
Taylor scored 17 goals for Burnley last season and won their 'Player of the Year' award.