The 19-year-old will today link up with Howe's squad in training and go straight into Cherries' squad for Saturday's League One clash with high-flying Carlisle.
Howe was forced to dip into the loan market for the first time this season due to doubts over the fitness of Lee Bradbury and Stephen Purches.
I have been aware of Adam for a long time, said Howe. I watched him for the first time in a pre-season friendly about two-and-a-half years ago and he impressed me straight away. He is someone we have always kept tabs on and we are delighted to bring him here.
Smith, who has progressed through the ranks at White Hart Lane, served Wycombe and Torquay on loan last season, turning out for the Gulls in their 2-1 defeat at Dean Court in December.
Howe added: We are fortunate to have two very good right-backs but unfortunate that we have lost them both to injury at the same time. We are lucky that we are in a position to bring in a loan player as cover. Hopefully, Adam will enjoy his time with us and his stay will benefit both parties. He impressed again when he played for Torquay against us last season.
I would like to thank Harry Redknapp, Kevin Bond and Tim Sherwood for their help in making the move possible. As a club, we would also like to thank Spurs.
Neither Bradbury nor Purches has trained so far this week and both are doubts for the visit of Carlisle on Saturday and for Cherries' Dean Court showdown with Exeter on Tuesday.