The transfer appeared to be cancelled at the end of July when the Romanian club's incarcerated owner reacted furiously to Spurs' negotiating tactics, but it has now been resolved
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The 23-year-old now looks set to complete a transfer, reportedly in the region of £8 million, after Becali gave his blessing.
"It was Becali's wish to let the media know about the transfer, he told us to announce it to everybody," Stoica told reporters.
"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 hopes Chiriches will play a part in the club's Champions League play-off second leg clash with Legia Warsaw on Tuesday before completing his move.
"Chiri's condition is good," he told a press conference broadcast on Digi Sport 1. "I'm very happy for him. I told him to have patience and trust. I hope he will help us on Tuesday evening.
"The club made money on the deal and I'm sure it will lead to a greater team. I cannnot 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."
Romania coach Victor Piturca has already given his blessing to the transfer and has tipped Chiriches to thrive in the Premier League.