He is the third player within the space of 24 hours to make the move from the Kent club to the south coast, following the arrivals of Sam Magriand Danny Kedwell.
Dury also represents manager Paul Doswell’s 11th new arrival at Westleigh Park since replacing Lee Bradbury as manager since the end of last season.
The Westleigh Park boss regards Drury as another important part of the jigsaw as he prepares his new-look Hawks side for their return to National League South.
Doswell said: 'Jukebox (Drury) is another player I have known for a long time.
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'I know all about his quality on the ball from his games against us at Sutton United.
'He makes great runs into the box and is the sort of player who will fit into my system well.
'Earlier in his career he made a big money move to Ipswich Town.
'But he is still the sort of player who will play a game in the park.
'Like me, he just loves his football.
'He is another great character and still someone desperate to be successful.'
Drury made his £150,000 move to Portman Road in January 2011, after excelling at Luton Town.
He made 62 appearances for Ipswich during a two-year spell.
Since being release from the Tractor Boys in 2013, Drury has given good service to Crawley Town, Luton again, Eastleigh and Ebbsfleet United.