The former Middlesbrough and England U-21 manager had been expected to complete the deal today after a four-game interim spell, in which he won two and drew two of his games.
Southgate has signed a four-year contract as manager of the Three Lions and the deal is reportedly worth £1.5m per year.
Southgate said that he was "extremely proud" to be named the full-time England manager but wants to simply concentrate on "getting the job done".
"I am extremely proud to be appointed England manager. However, I am also conscious getting the job is one thing, now I want to do the job successfully," he said.
"I'm determined to give everything I have to give the country a team that they're proud of and one that they're going to enjoy watching play and develop".