Spurs are yet to confirm the transfer, but Steaua general manager Mihai Stoica claimed on Saturday night that Chiriches, a 23-year-old international centre-back, will make a reported £8 million move to White Hart Lane.
The deal had been expected to go ahead early in the summer, but Spurs' hopes of landing the player were dashed when Steaua's owner Gigi Becali - who is currently serving a prison sentence for defrauding the state in a series of land deals - ordered the club not to sell.
But Becali has now apparently had a change of heart, and the deal is now going ahead after all.
"It was Becali's wish to let the media know about the transfer, he told us to announce it to everybody," Stoica said. "We had to tell Vlad the deal was done. He was with us all day, it was correct to announce it to him."
Steaua manager Laurentiu Reghecampf expects the player to turn out for the side one more time in their Champions League qualifier second leg against Legia Warsaw on Tuesday before heading to London.
"I'm very happy for him. I told him to have patience and trust. I hope he will help us on Tuesday evening," Reghecampf said.
"The club made money on the deal and I'm sure it will lead to a greater team. I cannot say the amount for which he transferred, but is very high, he'll be the most expensive transfer in Steaua's history. He will remain in history of the club if we manage to qualify for the Champions League."