Rangers chairman Andrew Cavenagh acknowledged the recent testing period for the club – during which the board was criticised by fans for the drawn-out search for a manager – but said Rohl can “restore pride and ultimately success”.
“Danny’s experience at elite level, in high-pressure environments, makes him a strong fit for what we expect here,” said Cavenagh.
“We know the past few months have been challenging, but our focus has always been on getting the right person, who is ready to immediately embrace this football club and the demands that come with it.
“Danny impressed us with his vision, his character, and his understanding of what Rangers stands for. We believe he can help restore pride, momentum, and ultimately success.”
Rohl, who left 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.
Rangers vice-chairman Paraag Marathe said the club had been through “a thorough process to ensure we identified the right person” and praised Rohl’s “tactical intelligence and hunger”.
Former Southampton boss Martin was sacked with Rangers eighth in the league, nine points behind champions Celtic and 11 adrift of leaders Hearts.
They are now eight points behind labouring Celtic and 13 behind Hearts.
Rangers also failed to qualify for the Champions League under Martin and lost both of their Europa League games.
Rohl assured Rangers fans he is ready to embrace the expectations of fans who have witnessed Celtic’s domination – 12 title wins in 13 years – in recent times.
“The expectations are huge and I love this challenge because I set high standards for myself and the team too,” he said.
“Rangers is built on a tradition of hard work, unity and success. That is exactly what you will get from me and what I want my team to represent for all of you.
“I’m looking forward to meeting the squad and getting down to work ahead of Thursday’s game away to Brann.”
