He is the first signing for Leeds' new coaching team of Andy Key and Neil Back, who are preparing to mastermind an immediate Premiership return following the Yorkshire club's relegation to National League One last term.
Welshman Strange, 34, spent four seasons with Bristol, amassing 825 points. His previous clubs include Rotherham, Newport, Llanelli and Pontypridd.
He said: "It is going to be a tough challenge, but it is a great opportunity for me, and hopefully I will be able to help Leeds Carnegie get back to where they need to be."
Strange will join fellow new recruits Henry Paul, Phil Murphy, Scott Barrow, Jon Pendlebury and Pete Bucknall at Headingley as Leeds build towards the new campaign.