Manchester United boss Louis van Gaal has reiterated his desire to keep David de Gea at Old Trafford.
QPR are interested in signing West Ham midfielder Mark Noble, Sky sources understand.
The Scotland Under-17s coach will take charge of the League One side at the start of next month after winning the race to succeed Martyn Corrigan.
Chairman Bill Darroch told the club's official website: "We received a number of high quality applications for the job and the board felt that Scott had the right approach and the right mix of attributes that best meets the vision and aspirations of Stenhousemuir Football Club.
"We believe that the attributes he brings as a former player with considerable professional playing experience, coupled with his passion for youth development, will be a perfect fit for Stenhousemuir."
Booth added: "Everyone in Scottish football knows that Stenhousemuir is a modern, progressive club with big ideas on moving the game forward in Scotland.
"Be it their award-winning community programme, or their new youth academy concept, Stenhousemuir is a club that often leads the way in developing the game.
"I am looking forward to being part of the club and doing my bit to take the club forward."
Interim coaching team Brown Ferguson, Robert Glen, David Rowson, Ross McMillan and Scot Buist will continue in charge for the matches against Rangers, Airdrie and Forfar before Booth takes control.