The 34-year-old World Cup winner, who is currently an HSBC ambassador for the 2009 Lions tour to South Africa, will be assisted by Phil-Keith Roach and Kingsley Jones.
Roach, the scrummaging coach during England's 2003 World Cup triumph, will become forwards coach, while Jones, who is currently in charge at the Stockport-based club, will move up to the director of rugby role vacated by Philippe Saint Andre earlier this season.
The head-coach role will be Robinson's first coaching position having only retired from the playing side of the game at the end of last season.
"It's fantastic news for the club that Jason has agreed to join the coaching staff," said Jones.
"It's no coincidence that the three years that Jason was captain was the most successful in the club's history.
"Jason has been a professional since the age of 16 and everything he has done in both codes, he has been successful at.
"He is renowned for his enthusiasm and drive and is a proven 100% winner. He also has great mentoring skills which will prove invaluable in his work with the senior and academy players at the club."
Robinson, nicknamed Billy Whizz because of his famously-fast feet, scored five tries on his Lions debut eight years ago before adding a stunning individual effort during the opening few minutes of the Lions' first-Test win over the Wallabies in Brisbane.
He went on to tour once more in 2005, playing in the first and second Tests against the All Blacks to finish his Lions career with five Test caps and a total of 11 tries in 11 Lions appearances.