The Belgium international, 27, scored 25 goals in 119 games for Spurs and has signed a four-year contract at the Hawthorns.
The Baggies’ next arrival could be £15m-rated Spanish midfielder Ignacio Camacho of Malaga, while England Under-21 striker Saido Berahino’s future remains uncertain ahead of Wednesday night’s deadline.
“I said last week that these signings all had to be about players who would improve our squad and Nacer does precisely that,” said West Brom boss Tony Pulis. “He’s a top player and I’m delighted we’ve got him.”
Chadli said: “I feel very good to be here. It came very quickly but I spoke to the club and they have a good team, a good manager and I am very pleased to be here. I just want to help the team win as many games as possible.”
Defensive midfielder Camacho, 26, is believed to have asked to leave Malaga, while Stoke and Crystal Palace have pursued former Tottenham target Berahino.
Spurs hope to replace Chadli with Wilfried Zaha, but have yet to persuade Crystal Palace to sell the former Manchester United winger.