Chiriches, 23, is expected to move to White Hart Lane next week after making his final appearance for Steaua in their Champions League playoff 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 told reporters.
"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."
It is understood that Spurs will pay Steaua a transfer fee in the region of £7m.