De Zerbi is set to take charge of his first game on Sunday at Sunderland. Significantly, De Zerbi begins with Spurs sitting in the relegation zone after West Ham's win against Wolves on Friday night.
A win for Spurs will see them swap places with the Hammers and Poyet told Tribalfootball.com: "I think that appointment is one of the best that they could have made.
"Obviously, the situation is particularly difficult. Now, it depends on how quickly he can change the situation.
"But yeah, I thought it was a great appointment. I think it was a good decision. I think the coach should be happy because the club pushed a lot for him. They pushed for him really strongly.
"That sends a message to the fans as well: 'This is our number one and he's coming. It doesn't matter how'.
"So all those things for me as a coach, I think they are great for everybody. So let's hope it works."
Poyet also hopes having a long-term appointment now in place will also ease the tension between the players and Spurs support.
Things have been toxic at times between those in the stands and those on the pitch - something Poyet has been monitoring closely this season.
The Uruguayan great also said: "The problem nowadays is, first and most, I think we're losing a little bit in the sense of what is football about.
"When I came to England in 1987, I knew 100% that if I was showing every week that I was giving 100%, the result was the consequence. Now I think we're putting it the other way around.
"Now we're saying the result is everything and it doesn't matter what you do. If you lose, you're rubbish. That's the social media situation. In the social media, every 100 posts after a game, 98 are negative. And that makes it a big thing. And everybody is agreeing on that.
"Me, I don't pay attention to social media, I pay attention to the players. Are they giving the maximum? Yes, for me, yes. Now, are they playing at their maximum capacity? No. And no, because they are confused. Which is normal as well, in the situation they are in..."
- Gus Poyet was speaking to Tribalfootball on behalf of Gambling.com where users can find a new trusted online casino