The Merseyside club announced they had given the 28-year-old permission to speak to Spurs, who had an initial offer turned down last week.
Pienaar, who is out of contract at the end of the season, would now seem to have a choice between Spurs and London rivals Chelsea, who have already had a bid accepted by Everton.
An article on Everton's website read: "Everton can confirm they have agreed terms with Tottenham over the possible transfer of Steven Pienaar."
Spurs have been considered the favourites to land Pienaar but appeared to be at loggerheads with Everton over a transfer fee.
The north London club were initially thought to have bid ¦pound;2million while Chelsea were prepared to offer a more acceptable ¦pound;3million.
Spurs manager Harry Redknapp said he was unsure whether that figure could be matched but it has been reported that a compromise figure of ¦pound;2.5million might have been offered.
Everton's acceptance would now appear to clear the way for Pienaar to move to White Hart Lane if personal terms can be agreed.
The Toffees have decided to cash in on Pienaar now to avoid losing him on a free transfer in the summer. He rejected a new contract at Goodison Park some time ago.
Source: PA
Source: PA