Defender Kirk Broadfoot and keeper Neil Alexander can also go on free transfers, should they choose to do so.
And Romanian stopper Dorin Goian also has the option of quitting for a cut-price £500,000, if he wishes, before this transfer window slams shut at the end of August.
SportTimes can reveal that USA skipper Bocan-egra and Bedoya negotiated free transfer clauses when they took big wage cuts back in February after the crisis-hit club plunged into administration.
And Edu can also leave thanks to a cut-price £300,000 clause which can be activated by interested clubs.
The USA trio – who have all transferred over into the newco – were signed for combined transfer fees of £3.5million.
But Rangers will now receive less than a tenth of that sum as they are all believed to see their futures elsewhere.
Bedoya is not due back at Murray Park until July 9. but has told friends he expects to depart, while Bocanegra and Edu have a further week's leave after that due to their international exertions.
Sources close to the American stars doubt whether they will ever be back in Scotland, with their agents actively working on moves.
Goian has transferred over to the newco and has intimated he will wait and see what league the club are playing in before he makes a decision on his future.
However, in return for taking a 75% wage cut, the former Palermo man has a clause that he can go for £500,000 in the window and that option may yet be taken up.
Broadfoot and Alexander, who both reported back for pre-season yesterday, can also go on a free during the remainder of their contracts if they take that option as a result of their wage sacrifices.
Edu has dropped massive hints he could join the 10 stars who have already walked away from the newco, which has cost the club some £25m in market value transfer fees.
He said: "I'm no different than anyone else. You want to go as far as you can in the game.
"It's a short career, you know. You want to try and play at the highest levels possible and test yourself against some of the best players."
And the ex-Toronto FC star admitted he can't believe the incredible way the season panned out for Rangers.
He said: "I tried to stay away from it as much as possible, tried not to read the papers, tried not to watch TV, but at the end of the day it was around you all the time.
"You come to training and there's a million cameras waiting for you. I tried to avoid it and just get the updates from the club, which wasn't always the easiest thing because sometimes it would come out in the press before we would hear about it.
"It was a situation that was weighing on our minds, and is still weighing on our minds because nothing is finalised. The fact that it's dragged makes it an uneasy situation to be in."
Rangers' shadow squad were back at Murray Park today for day two of pre-season.
13 players in total have reported back; Broadfoot, Alexander, Lee McCulloch, Lee Wallace, Kyle Hutton, Ross Perry, Kal Naismith, Darren Cole, Kane Hemmings and Scott Gallacher.
Free agents Andrew Mitchell, Salim Kerkar and Chris Hegarty – whose contracts expired at the end of May – also reported for fitness tests and it remains to be seen whether they will be offered deals.