The 23-year-old Romania international has been a target for Spurs all summer but a deal looked to have fallen through at the start of this month.
Now the two clubs look set to announce a deal of around £7million in the coming days for the highly-rated defender.
Steaua coach Laurentiu Reghecampf has now revealed that Chiriches is set to join Tottenham after their forthcoming Champions League play-off second leg with Legia Warsaw on Tuesday.
"Chiri's condition is good and the clubs have agreed to transfer him. I'm very happy for him," Reghecampf said after Steaua's 2-2 draw with Gaz Metan Medias on Saturday evening.
"I hope he will help us on Tuesday night and of course that he stays healthy.
"The club made money on him and I cannot say the amount for which he is transferred, but it is very high."