The South Africa international spent the second half of last season on loan at Goodison Park after failing to impress under then-Spurs manager Harry Redknapp.
He only signed for Tottenham last year after spending four years, the first of which was on loan from Borussia Dortmund, with Everton.
Opportunities were limited for Pienaar at Tottenham, where he started just five Premier League matches.
But he excelled on his return to Everton, scoring four goals in 14 league games to help them finish seventh, with manager David Moyes stating at the beginning of the month that one of his aims was to re-sign Pienaar.
"We are keen [on Pienaar] and I hope in time we would be able to conclude that deal," he said.
"I don't know if the situation has changed [with Andre Villas-Boas coming in as new Spurs manager] but Steven has made it very clear he wants to come back here and my understanding is that hasn't changed. My next job in the coming weeks is to get Steven Pienaar here as well."
Pienaar made no secret of his desire to return to Merseyside and Tim Cahill's move to Major League Soccer outfit New York Red Bulls paved the way for the 30-year-old's comeback.
He told the club's website: "I am happy to be here. It took a few weeks to sort out but I am delighted to be back and excited to play for Everton.
"There was no doubt in my mind that I would be back here. At the end of the season I told the manager how I felt and I am happy now it is all done."