Swann told BBC Radio Humberside the 44-year-old will replace sacked Russ Wilcox on Monday.
Caretaker Andy Dawson will take charge of the side, who are 23rd in League One, for Saturday's trip to Gillingham.
"I'm delighted because the most important thing was to not leave the team in limbo," Swann said.
"We've spent the last 24 hours ironing out the contract and we're there now so we hope to announce the appointment on Monday.
"I was impressed with Mark's track record and I hope he has a long tenure here. It's a great opportunity for him and for us."
Wilcox was dismissed on Wednesday, following the Iron's 2-1 defeat by Notts County in the Johnstone's Paint Trophy.
He led the club on a 28-game unbeaten run during their promotion campaign last season, but only managed four wins from 15 matches this term.
Robins has been out of the game since leaving Huddersfield in August, the day after the Terriers lost their opening game of the season 4-0 to Bournemouth.
The former Manchester United striker spent 18 months at the John Smith's Stadium and has also managed Rotherham and Barnsley.
His first match in charge of the Glanford Park side will be against Colchester on 18 October.