The 19-year-old Mexico international could join the Premier League side as early as today according to Sport after Barca accepted a £6.2million bid.
That fee may rise to £8.6million depending on both Dos Santos and Spurs meeting specified targets during a four-year stay at White Hart Lane.
Dos Santos's father, Zizinho, admitted that his son is proud and excited by the thought of moving to such a prestigious club as he told Mexican daily paper, Record, that a deal was in the offing.
"Nothing has been finalised," he said. "But it is an honour that a club as important as Tottenham want to sign Giovani, but nothing can be said officially yet.
"The ambitious project that Tottenham have has excited Giovani and he just wants to go there and help the team in any way he can.
"It is obvious that leaving Barcelona is a risky decision, but with his qualities it appears that it could be the best option for him."