Rangers chief executive Patrick Stewart, who led the head coach search along with Thelwell, said Martin was the “standout candidate”.
The Ibrox club spoke to former Real Madrid assistant manager Davide Ancelotti and former Feyenoord manager Brian Priske, while former manager Gerrard and ex-Ajax head coach Francesco Farioli were among those also linked with the post.
“Our criteria were clear: we wanted a coach who will excel in terms of how we want to play, improve our culture, develop our squad, and ultimately win matches,” Stewart said.
“This appointment is about building a winning team and a strong culture. He is no stranger to our club, we expect success and Russell knows that. We are excited for his leadership.”
Thelwell suggested Martin’s time in the Premier League “has sharpened his approach, both tactically and personally”.
Giving an insight into what a Rangers team under Martin will be like, he added: “His teams play dominant football, they control the ball, dictate the tempo and impose themselves physically. They press aggressively and work relentlessly off the ball.
“These are all characteristics that we believe are required to be successful at home, away and abroad.”