The match at the Aviva Stadium will be the first time England have played in the Irish capital since crowd trouble caused the referee to abandon a friendly between the two sides after 27 minutes in February 1995.
Next summer's fixture is scheduled a week before England face Slovenia and the Republic tackle Scotland in Euro 2016 qualifiers.
The Lansdowne Road riot was one of the darkest episodes in the history of English football, as right-wing extremists among the away fans threw objects onto the pitch after David Kelly had given the hosts the lead, prompting Dutch official Dick Jol to lead the players off the pitch.
However, the two teams met at Wembley last May, with no crowd trouble during the 1-1 draw.
The two nations have faced each other 14 times before, with England winning five and losing two of those games.
Club England managing director Adrian Bevington said: "While inevitably the focus for Roy and his team is on Brazil and the World Cup, we are always planning further ahead and we are delighted to announce this fixture next summer.
"We have had recent visits to France to begin initial plans for that tournament, and our friendly matches will also form a key part in the qualification campaign and preparation.
"It will be a significant moment for England to play in Dublin again, and due to the hard work by both organisations on many fronts we fully expect it to be a fantastic occasion enjoyed by both sets of fans."