Southgate has respect for the 61-year-old former Wimbledon and Nottingham Forest boss and believes he now has just reward for his efforts since succeeding Kevin Keegan.
Southgate said: "Joe has given them a direction now. It is brilliant for him, he deserves that for what he has done.
"I'm sure he that is what he hoped for when he got the opportunity in the first place.
"I'm sure he didn't think this opportunity would come along at this stage but he has grabbed it and good luck to him.
"Everybody knows the quality of players they have got and we will need to be at our very best to beat them."