Sharp, 25, signed for Saints on Monday evening to bring an end to his two-and-a-half years with Donster.
"It's a massive club with huge ambitions, and that is the main reason. The gaffer and his coaching team was another reason and it felt right in my head too," he said.
"I can't wait to get on with the challenge. I am delighted that I am here and joining a really big club with a strong squad of players, hopefully I can be a cog in the team that helps get this huge club into the Premier League."
The fee is undisclosed, but Sharp has signed a three-and-a-half year contract at St Mary's.
Sharp spent two seasons at Glanford Park, helping the Iron win the League One title in 2007 under the guidance of Adkins, who himself swapped North Lincolnshire for the South Coast at the start of last season.