Marketing previously reported that negotiations were at an advanced stage.
Alex Horne, FA general secretary and Peter Hope, Vauxhall marketing director, are expected to disclose details of the sponsorship next week. The deal could be worth as much as £5m a year.
Vauxhall will replace Nationwide, which ended its 11-year sponsorship of the England team earlier this year. The car marque has also ended its sponsorship deals with Wales, Northern Ireland, and Scotland.
It is unclear if the deal with Vauxhall will expand to the other home nations.
The deal with Vauxhall could conflict with the FA's existing arrangement with Fiat, the official car supplier to the England team.
In December last year, the FA announced that David Bernstein, the former chairman of Manchester City, would become its new chairman.
The FA had been without a full-time chairman since David Triesman left in May 2010 after making controversial remarks about rival bidders for the 2018 World Cup.
The FA declined to comment and Vauxhall was unavailable for comment.