Spirit chief Remo Nogarotto said the deal was subject to approval by the Scottish Football Association and Soccer Australia, but he did not foresee any problems.
Ibrox officials agreed a 51% controlling interest in the Sydney club, believed to have cost £1m, after days of talks in Australia.
Details are expected to be completed within the next seven to 10 days.
Spirit chief Remo Nogarotto said the deal was subject to approval by the Scottish Football Association and Soccer Australia, but he did not foresee any problems.
"The parties have agreed to terms, the contract terms are being drawn up by our lawyers and should be signed by next week," he said.
Nogarotto saw the deal as a precursor for future European links with Australian soccer.
"Glasgow Rangers are one of world soccer's super powers and they have shown leadership in breaking away and investing into the game," he said.
"A deal like this brings capital, and with that bigger opportunities for us to nurture and help our talent stay here.
"This gives us a better chance of offering the level of wages that are on offer in Europe."
Rangers chairman David Murray announced his hopes to take a controlling interest in the Australian side aimed at giving their brand name a global reach two weeks ago.
As well as the marketing aspect of such a deal, Spirit may be used as a feeder club to the Ibrox club, who already have two Australian internationals in Craig Moore and Tony Vidmar.
Spirit had a poor season, finishing 13th in the 16-team league and troubled by dwindling crowds in their second season in the NSL.
Norwegian on the move
Meanwhile, Rangers out-of-favour Norwegian international defender Stale Stensaas could be on his way back to his old club, Rosenborg.
Stensaas, 28, will meet officials from the Norwegian champions next week and Rangers have said he can end his unhappy three years at Ibrox.
"The clubs have agreed terms," said Rangers manager Dick Advocaat.
"Now he will go to Rosenborg on Monday and have personal negotiations."
Rangers paid Rosenborg £1.75m for Stensaas in June 1997 but the full-back only made 21 league appearances in his first two seasons before being loaned to Nottingham Forest.
Dutch colony
Holland international defender Bert Konterman has told the media Rangers are keen for him to join the ever-growing ranks of Dutchmen at Ibrox.
Right-back Fernando Ricksen has already been secured for next season and Dick Advocaat is also interested in bringing in the £3.5m-rated Feyenoord star.
Konterman, 29, will play for Holland in this summer's European Championship finals and his valuation could change if he was to catch the eye.
Rangers could, however, face a battle for his services with a number of Premiership clubs already being alerted to the situation.
Konterman said: "I know there has been interest from the Premiership, but I know Rangers are very interested."
David Murray does not expect an answer from Juventus on the availablity of Yugoslav striker Darko Kovacevic until the conclusion of the Italian season.