The Baggies have won the race for the 19-year-old hot-shot amid interest from several rivals.
Lankshear is rated as one of the top prospects in his age group in the country.
The teen has made six appearances for Tottenham’s first team and scored his first goal this season, away at Galatasaray - a Europa League clash in which he was also dismissed.
He is not registered in time to face Plymouth on Saturday lunchtime but could make his debut against Sheffield Wednesday next weekend.
Lankshear, who will join up with the squad on Monday, said: "I am delighted to join this great club. I'm looking forward to meeting my new team-mates and I can't wait to play in front of all the fans.
"This is a fantastic opportunity for me to compete for game time and, hopefully, score goals that can help the club push on to get promoted during my time here.
"Tony Mowbray is a manager who everyone says only good things about and I’m keen to learn as much from him as I can over the next few months."
Lankshear becomes Albion’s second signing of the January window after the £2.5million addition of Isaac Price.
The frontman scored 23 goals and was Premier League 2 player of the season last term.
Sporting Director Andrew Nestor added: "We have felt since the summer that we would need to prioritise the addition of another striker in this window and we are pleased now to have brought in Will, who we have been watching for some time and has been among our top targets for reinforcement in this area.
"We had spoken to his club prior to January and have had to be patient as agreeing loans often tends to materialise later in the window due to individual club circumstances.
"We can now look forward to having Will as part of our squad and we all believe he has the capability to make an important contribution between now and the end of the season."
He is believed to have been Albion’s top target in that area and was much sought after by several Championship clubs and overseas.