Drury has netted eight times in 26 games for the Blue Square Bet Premier side this season.
"For the money we got him for and his ability I think it's a really good deal and a really good addition," Town boss Paul Jewell told BBC Radio Suffolk.
"If Andy gets in and gets a chance I don't think he'll disappoint people.
My only worry is that he is 27 and has never played league football in his life
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"He can play right-side and left-side of midfield and down the middle, he's a good technician with a good delivery from dead balls."
After helping Stevenage to promotion to League Two last season Drury turned down a new contract at Broadhall Way and chose to drop back down a division to join the Hatters.
He had two years at Stevenage, scoring seven goals in 57 league appearances, after spells at non-league outfits Sittingbourne, Eastbourne and Lewes.
Source: BBC Sport
Source: BBC Sport