The deal appeared to have been concluded last week after a bitter war of words between Steve Gibson and Ian Elliott, Downing's agent.
The England winger, a long-time target of Spurs, said: "The contract is all agreed but there are still some things to iron out. It should be done any time this week.'
He added: "You can get unsettled because there is a lot of talk. I'm glad it's out of the way and I know where I'm going to be playing my football.
"I think the team is on the up. That's what the manager has said and there are players he is going to bring in."