Sharp was due to head south on Monday to discuss personal terms with Adkins and assistant Andy Crosby, with whom he worked at Glanford Park - helping the Iron win the League One title in 2007.
He moved back to his boyhood club Sheffield United that summer, before joining Doncaster in July 2010 after failing to break into the Blades' team.
"I'm disappointed to lose my top scorer and hopefully one day we'll be able to keep our better players," said Rovers boss Dean Saunders.
"I wish him all the best, he's been brilliant for the club and for me. We have to move on now and the rest of the players in the squad should see this as an opportunity to step up.
"I now have to speak to the chairman to see if any of the money we get can be re-invested into the team."
Sharp is not the first former Iron player to be reunited for Adkins at St Mary's.
Last January he signed Jonathan Forte from United, while he has also had a number of bids for Gary Hooper rejected by Scottish Premier League side Celtic.
Hooper netted 50 goals for Scunthorpe after being signed by the-Iron boss Nigel Adkins in July 2008 for £175,000.
He moved to Celtic two years later in a deal believed to be worth around £2.4million.