Dempsey's future had been uncertain after he announced his desire to leave Fulham and reportedly 'went on strike', refusing to play until he was granted his wish.
He has admitted that not knowing where he would be plying his trade after the transfer window closed was a difficult situation for him to manage.
"I just remember calling my wife and my mum and almost wanting to break down in tears because it was a tough time," he said.
"Going into that last day and night there were still a lot of question marks. It wasn't clear-cut this was going to happen.
"Some other things came up and you are going through that struggle, which was not fun for anybody. It was difficult for Fulham and for me, not knowing how it's going to end."
Dempsey could make his Spurs debut when they return to Premier League action against Reading next Saturday.