The former Hearts duo have begun training with Ally McCoist's side with a view to penning deals with the club that would see them plummet through the leagues to Scotland's bottom tier next season.
Rangers' future should become clearer today, with the transfer of their SFA membership and potential registration embargo on the verge of being sorted out, and McCoist is pressing on with plans to strengthen his threadbare squad.
Beattie and Black could be the first two pieces of the Gers jigsaw, and Dodds reckons the pair will become instant idols with the Ibrox crowd.
He said: "I think it is a no-brainer that when players come to Rangers, the fans will take them on board straight away.
"They will have shown a commitment to the club to drop down from the SPL to the Third Division.
"They are joining a big club, but the Third Division is ideally not where they would want to play.
"They will know the standard of football isn't going to be great, but they will want to join Rangers because of the club.
"They will be heroes right away."
Signing former Gorgie stars Beattie and Black would be a major coup for McCoist as he begins the task of building a squad that may have to see him through both the Third and Second Division title successes.
The Gers will have their sights firmly set on a rapid rise through the leagues and a quickfire return to the SPL and Dodds reckons any new arrivals will be thinking long-term.
He said: "Make no mistake about it, Black and Beattie are too good to be playing in the Third Division.
"But they will see what is at the end of the tunnel. In three years, Rangers could be back in the SPL.
"They are the right players for Rangers.
"They can see three promotions in three years and that is attractive to them."