The 19-year-old's transfer was completed prior to their Championship opener against Peterborough but the player is suspended following a dismissal for Spurs' reserves last season.
Livermore, who scored for Spurs against Barcelona in the Wembley Cup in pre-season, will also miss the next three games and won't be available until the home clash with Plymouth on Saturday, August 22.
Boss Nigel Clough told the club's official website: "He is a big, powerful, energetic midfielder and someone we believe can do an important job for us.
"He is only young and still learning the game, which is why Tottenham are prepared to let him come out on loan to us. We want to keep him until Christmas at least and see how it works out for both parties.
"The midfield is definitely an area where we need an extra body and we are happy to have concluded this deal."