Morecambe were promoted into the Football League after beating Exeter City in the Conference Play-Off Final at Wembley, with Dagenham & Redbridge claiming top spot in the league.
Newby 28, a former Blade loanee impressed after a successful trial, he had previous had a spell at Southport before being released.
He joined United on a three month loan from Liverpool in August 2000 and played only three games (plus 10 as a sub) without scoring a goal. He has also represented Carlisle United (loan), Crewe Alexandra (loan), Bury, Huddersfield Town, York City, Kidderminster Harriers and Wrexham.