The former England Under-21s boss became the leading candidate for the role after he oversaw two wins and two draws during an interim spell in charge of the Three Lions.
There were reports that negotiations had hit a snag because of a release clause that would allow the FA to sack Southgate after the 2018 World Cup.
The former Middlesbrough boss was understood to be reluctant to sign, and now it appears that the idea has been completely scrapped.
In his first press conference since the appointment, Southgate told reporters: "There is no break clause in my contract. I want to be successful in this role."
The former footballer's first official game as England manager will be a friendly with Germany on March 22.