Murray was appointed to the board after a consortium led by Englishman Charles Green completed the purchase of the Glasgow outfit on Thursday.
The new chairman is a season ticket holder at Ibrox and has boardroom experience at Manchester United, where he previously held a 25 per cent stake.
The 57-year-old believes his background will help him revive Rangers while providing the financial footing which he insists is vital in re-establishing the crisis-hit club.
"It's a fantastic honour. I can't be a player now and I can't be the manager so being chairman is probably the best thing I could do," Murray told Rangers TV.
"We need to bring financial stability, probity and transparency to this football club and bring our great name back to the reputation it had.
"Since Valentine's Day, I've probably been awake every night over things here, as everyone in this great stadium has been.
"Hopefully I'll bring integrity and honesty to my position. I've been involved in taking big stakes in companies and helping the management in the past.
"Of particular relevance is the Manchester United stake. I was equal to Martin Edwards [in terms of his holding] at the time. I worked with him and David Gill for many years.
"It was an iconic, global brand and that's what Rangers is. With a different Sky deal we'd be just as big."
Much uncertainty over Rangers' future still remains though, with a vote set to take place next month which will decide if the club is granted a place in next season's Scottish Premier League.
July 2 is the earliest date that a meeting between the SPL clubs can take place to decide on Rangers' future and Murray ackowledges that any planning has to be put off until then.
"There are so many uncertainties that it's difficult to say what our business plan is. We don't know what league we're playing in and we have to take some sort of punishment," he added.