Now the Northern Ireland internationalist is hoping to help the gap left behind by his countryman after becoming Ally McCoist's second summer signing as he agreed a four-year deal with the Irn-Bru Third Division club.
Having watched Davis quit the Ibrox outfit to sign for Southampton, Shiels can't wait to fill the gap left in the Rangers midfield. He said: "I see myself as a midfielder. I'm obviously willing to play anywhere Ally McCoist needs me, but I certainly think I can play in midfield and get forward into the penalty area.
"I've been very good friends with Steven since we were nine. He's only got good things to say about this club and I know, from speaking to him all summer, that it was a big wrench to leave.
"That is what he had to do, what was best for him and his family. My dad knows him, he coached him when we were younger, and I know how bad he felt having to leave."
Shiels is also aware his arrival maintains Rangers' connection with Northern Ireland on the back of the departures of Davis and Kyle Lafferty, and he sought the opinion of international boss Michael O'Neill on the move.
He said: "I come from a Rangers community and I have friends who are season ticket holders and come over on the boat every weekend. So I have grown up with Rangers.
"I have also been in touch with Michael all summer. He knew this was an option that I was considering and he has been nothing but supportive throughout the process. He has been in Scotland and played in this country and he knows the game here."
Eyebrows will, most likely, be raised at a player's decision to leave the SPL and also reject the opportunity to play at a higher level in England or abroad to play Third Division football here.
Shiels, however, insists the lure of the Ibrox club and the added bonus of playing in front of such a passionate support made it a no-brainer when he came to making one of the most important decisions of his career.
Meanwhile, Ally McCoist hopes to find out within the next 24 hours whether Craig Beattie will join Rangers. The Ibrox club have tabled an offer for the former Hearts and Celtic forward, who has been training at The Rangers Training Ground.
McCoist faces a race against time to assemble a squad before a 12-month transfer embargo comes into effect on September 1, and he hopes to add Beattie to his list of captures after recruiting Shiels and Ian Black, and re-signing Andy Little.
McCoist told rangers.co.uk: "I have meetings with (chief scout) Neil Murray and chief executive) Charles Green tomorrow. We will push a few names forward and see where we go.
"Charles has spoken to Craig Beattie's agent and he made him an offer. As yet, I have not heard back from him or from Craig but, hopefully, I will do in the next 24 hours."
McCoist is also hopeful of retaining the services of defenders Carlos Bocanegra and Dorin Goian, who featured in Sunday's 2-1 Ramsdens Cup win against Brechin.
RANGERS GAME SWITCHED
RANGERS' Irn-Bru Third Division opener against Peterhead at Balmoor Stadium on Saturday week has been moved to a 12.45pm kick-off and will be shown live on Sky, while the Ibrox club's Ramsdens Cup second-round tie at Falkirk has been put back to Tuesday, August 21 at 7.45pm because Ally McCoist will have players on international duty.
Other Ramsdens ties: Tuesday, August 14: Queen's Park v Partick Thistle, Morton v QofS (both 7.30), East Stirling v Airdrie Utd (7.45).