The warrior, who is thought to have died about AD 500, was found buried at RAF Lakenheath in 1997 with a horse, bridle, sword and shield.
Forest Heath council has announced it will provide a grant of £789,813.
Peter Merrick, chairman of the Mildenhall Museum Society, said: "We're obviously delighted as lots of hard work has gone into it."
Suffolk's Archaeological Service has the skeletons of the warrior and horse, which were part of a cemetery containing 427 graves.
The horse's bridle is currently at the British Museum, but it will be returned for display in Mildenhall.
Mr Merrick said: "The British Museum's policy now is that locally found things should stay in their locality and not go into store in London, so we're tickled pink."
The museum refurbishment is costing £1.2m with the rest of the money already secured from the Heritage Lottery Fund.
Lizzie Cocker, arts and heritage officer at Forest Heath District Council, said: "The money's been sitting in our capital programme and it's been planned for four or five years, so it's a long-term development in that sense."
The intention is to display the warrior and horse as they were found.
Jo Caruth, senior project officer with the archaeological service, said: "Some of the very small bones have decayed and some of the bones have been destroyed in the process of radio carbon dating, but all of that is important in terms of understanding who the man was and his place in Anglo-Saxon society.
"We may be able to get some evidence to show if he's related to other people within that cemetery, but we can't actually say who he was.
"It seems very appropriate that he's going back to where he came from."
Work on the museum is due to begin in July and should be completed next year.
Mildenhall Museum is set to double in size to help display the remains of an Anglo-Saxon warrior and his horse.