The 46-year-old, based in Yorkshire, will be at the helm for the forthcoming World Cup qualifiers against Malta, Slovenia and Scotland as well as a friendly against Spain in a busy two-month period following the exit of Sam Allardyce on Tuesday evening.
The ex-Middlesbrough manager moves up from the England Under-21 side on an initial temporary basis and Mills insists that Southgate will be free of the pressure that his predecessors have come under.
Mills – who played alongside Southgate at Boro – said: “It is a good opportunity for Gareth with these four games. There is no real pressure.
“The first game is against Malta at Wembley and if he does well, he might have a chance of getting the job in its own right on a permanent basis – if he wants it, of course.
“I think Gareth will be a very good job in the next four games. He is a good and modern coach and buys into the psyche of the younger player and he understands and ‘gets’ them.
“The friendly against Spain is tricky, but the three qualifying games are all winnable games and there is no reason why it cannot be positive for him.
“What has he got to lose if it doesn’t go well? Although I think it will go well. But if it does not, it is not his fault and he has been thrown into a situation and we go from there.”
As recently as September 5, Southgate had expressed doubt that he would have been ready for the job, had the Football Association turned to him before Allardyce in the summer.
But following this week’s dramatic developments, allied to the fact that the FA are not exactly blessed with plentiful and realistic options, the landscape may well be irrevocably changed, according to Mills.
Mills added: “He (Southgate) never wanted it on a permanent basis before. But suddenly now, we are running out of options.
“That is the biggest problem and we went down the road of who is available before. It should be an Englishman and the FA decided that. They have just employed someone and must now find somebody else.”
Following Southgate’s elevation, Bradford-born Aidy Boothroyd – currently England Under-20 manager – will step up and take charge of the Under-21s for their final two European Championship qualifiers next month.