Former Hibernian and Kilmarnock midfielder Shiels penned a four-year deal with the Glasgow giants on Tuesday, while Black - a free agent following his departure from Hearts - joined at the weekend.
The pair are the first players to be recruited since Rangers were consigned to liquidation and voted into the Irn-Bru Third Division.
McCoist believes both will have a crucial part to play as the Ibrox side bid to climb through the divisions and secure a return to the SPL as soon as possible.
He told rangers.co.uk: "We are thrilled that Dean has agreed to come to us.
"He is very optimistic, the same as we are, that we can come through the leagues with a bit of style.
"We are all aware of how difficult that will be but it's a challenge that Dean is also looking forward to and it's a great boost for everybody at the club that somebody of Dean's quality has decided that he sees his future at the club.
"We know what we are getting, we are getting a very talented player who was quite rightly voted one of the best players in the SPL last year.
"I'm a little bit biased but I would include Ian Black in that category too.
"So they are two great signings and hopefully there will be more to come. It's a sign of the pulling power and the stature of the club that these guys want to join Rangers."
Rangers have also tabled an offer for former Hearts and Celtic forward Craig Beattie, who has been training at Murray Park.
McCoist faces a race against time to assemble a squad before a 12-month transfer embargo comes into effect on September 1.
He said: "I have meetings with (chief scout) Neil Murray and (chief executive) Charles Green [on Wednesday].
"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."