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The former Crystal Palace and Aston Villa defender replaces Steve McClaren who resigned at the end of last season to take over as England coach when Sven-Göran Eriksson steps down after the World Cup finals.
Southgate's appointment on a five-year contract will upset the League Managers' Association [LMA] who argue he must have the Uefa Pro Licence. But Middlesbrough chairman Steve Gibson decided that Newcastle United have set a precedent by promoting Glenn Roeder to head coach, even though he does not hold the badge either.
FA Premier League rules state coaches without the Pro Licence can only take charge of a club for 12 weeks but the top flight's club chairmen recently voted to allow Roeder dispensation.
The former West Ham manager had been enrolled on a Pro Licence course in the past but was forced to withdraw due to illness. He will now take the year-long course in order to be fully qualified by the end of next season.
Middlesbrough argued Southgate had been unable to acquire all of his coaching qualifications because of his playing career.
A statement from the LMA said: "The LMA has the greatest respect for both Steve Gibson and Middlesbrough Football Club
"The association has said all it wishes to say on the subject of mandatory qualifications and so will not be joining any public debate over coach licensing and the FA Premier League rules.
"The Football Association and the Premier League are the guardians of their own rules and it is up to those bodies to apply them."
Boro chief executive Keith Lamb said: "Middlesbrough and Gareth should not suffer because he has had such a successful career at club and international level.
"Until recently, Gareth has spent his summers serving his country as a player. It makes little sense such players should be denied rare opportunities like the one he now has simply because he hasn't had the chance to gain the qualifications."
The Premier League are to talk to both Middlesbrough and the LMA about Southgate's appointment.
A Premier League statement made it clear the rules which require a manager to have the Uefa Pro Licence.
A statement from the Premier League read: "In appointing Gareth Southgate Middlesbrough were fully aware that as our rules stand it is a necessity to have the Uefa Pro License or equivalent to manage in the Premier League.
"As Middlesbrough have stated, they are seeking discussions with the Premier League, FA and LMA to discuss this situation. We will, of course, take a full part in those discussions during the close season.
"In the interim, Middlesbrough have been able to appoint Gareth Southgate as their manager, as rule Q4 concerns team selection during the course of the Premier League season."
Gibson turned to Southgate, who won 57 caps for England, after talks with Terry Venables, Martin O'Neill and Alan Curbishley.
Meanwhile, Middlesbrough have agreed an undisclosed fee with Chelsea to sign Robert Huth, their German defender.
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