Nelson joined The Bees for a trial last month, as former number one Paul Smith was set to join Premiership side Southampton for £500,000.
The South West London club will pay the UniBond League Premier Division leaders £7,500 now and a further £2,500 in April, with Hucknall Town to receive a sell-on fee of 25 percent should the Griffin Park club move the custodian on in the future.
Nelson had been training with First Division high-flyers West Bromwich Albion last week before Hucknall Town chairman Brian Holmes accepted The Bees' cash bid for the keeper.
The player has since put pen-to-paper on a two-year, four-month contract with the Second Division side and Nelson is grateful to receive a fresh opportunity of playing League football.
"I've been fighting to get back into the League," Nelson told the club's official website.
"I went to Hucknall and thought if do well, maybe I've got a chance and I'm grateful to Brentford for giving me the opportunity."
