Ameobi spent part of last season on loan at Scunthorpe from Leeds United, but failed to make much of an impression with just 10 scoreless substitute appearances to his name.
The Leeds boss Gary McAllister decided he was surplus to requirements in the summer, allowing him to join their Yorkshire rivals Doncaster Rovers on a free transfer.
He is in line to make his Grimsby debut in their League Two game against fellow strugglers Barnet on Saturday, and has been given permission to line up against Scunthorpe in the JPT Northern Section second round tie on October 7.
Grimsby have had a poor start to the season, and are without a win in their opening seven League Two games. Stuart Watkiss is their caretaker manager after they sacked Alan Buckley, bringing to an end his third spell in charge of the club.
Tickets for the game against Grimsby Town on Tuesday October 7 (7.30KO) can be ordered now. Seating areas are all-ticket and are £10 adults and £5 concessions, with U-16s free. The terrace is pay on the gate at £8.