The 36-year-old German was in charge of Sheffield Wednesday between October 2023 and July 2025 following coaching roles with RB Leipzig, Southampton, Bayern Munich and Germany.
Rangers sit sixth in the Scottish Premiership, with just one win from eight games, and face Brann (17:45 BST) in the Europa League on Thursday.
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.
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 new manager, but believes 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.”
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”.
Rohl assured Rangers fans he is ready to embrace the high expectations of fans who have witnessed Celtic’s domination of the title in recent years.
“The expectations are huge and I love this challenge because I set high standards for myself and the team too,” he added.
“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.”
