“It is a huge privilege at an incredible club, recognised around the world,” said Rohl.
“I know it has been a difficult start to the season, but there is still so much to play for.
“The expectations here are clear. The fans want to see results now – my mentality and experience is to think in exactly the same way.
“We have no time to waste, we start straight away. I respect that trust is earned and understand we have to give the supporters confidence in what we are doing by showing it on the pitch from the start.”
Title-winning boss Gerrard withdrew from consideration last weekend, saying the timing was not right for him to return to Ibrox.
Rohl then also pulled out, leading Rangers to hold advanced talks with Australian Muscat – but the potential delayed start to his tenure made the deal unworkable for both parties.
Rohl, who left Sheffield Wednesday by mutual consent in the summer, twice staved off relegation with the embattled South Yorkshire club.
He finished 12th in the Championship in his one full season in charge – an impressive achievement given Wednesday’s financial struggles.
Former Southampton boss Martin was sacked with Rangers eighth in the league, nine points behind champions Celtic and two more adrift of leaders Heart of Midlothian.
They are now eight points behind labouring Celtic and 13 behind Derek McInnes’ side.
Rangers also failed to qualify for the Champions League under Martin and lost both of their Europa League games.
