Grant, who incurred the wrath of Scunthorpe fans after a series of petulant displays, scored 16 goals in League Two last season for Rochdale.
The Liverpudlian left the Iron despite signing a new contract last summer after being booed in a game with Yeovil at the start of last season.
At the time, former Iron boss Alan Knill stated Grant had 'broke down'
"After last Saturday's game, Bobby, when he came off, was distraught at the crowd's reaction to him," said Knill.
"He'd had some abuse through the game, and on Monday he more or less broke down.
"Bobby was adamant he couldn't play here."
Blackpool boss Paul Ince is delighted to be able to bring Grant to Bloomfield Road.
Pool boss Paul Ince told The Blackpool Gazette: “We have Bobby Grant in on Wednesday to hopefully get a medical done.
“That’s a big boost. He’s a very good player".