Weir, 43, who replaced Danny Wilson as Blades boss 11 days ago, has appointed Owen, 32, a former player with Wrexham, as his assistant manager of performance.
"Adam is one of the most respected men in his specialist field and I'm delighted that he's taken up the offer to join us here at Bramall Lane," Weir told the club's official website.
"With pre-season almost upon us it was imperative to get Adam in as quickly as possible to organise at this vital time."
Owen, who specialises in football-specific conditioning and injury prevention techniques, hopes to be one of the first coaches in Europe to obtain both the UEFA Pro Licence and PhD in Football Science.
"I've had seven fantastic years at Rangers and turned down other opportunities to work elsewhere to join David here at Sheffield United," said the Welshman.
"This is a big progression for me to come into a club the size of this as an assistant manager. The aim is, alongside David, to make sure we develop the club's on and off pitch processes."