The striker, who scored 19 goals in the SPFL Championship last season, has signed a three-year contract and will join up with former Livingston team-mate Stefan Scougall at the Skybete League 1 side.
"He has served his apprenticeship at Livingston, he scored a lot of goals and he needed a fresh challenge," said McGlynn of the 21-year-old who was wanted by Derby County in 2012 only for the proposed transfer to collapse.
"Marc has done it over the years for Livingston, he's ready for it. Everyone is looking for a goal scorer and that's what Marc is."
McNulty is now one of seven Scots at Bramall Lane alongside Scougall, Bob Harris, Ryan Flynn, Stephen McGinn, Neill Collins and Jamie Murphy.