Robinson made 38 appearances last season, scoring 10 goals, and the 33-year-old was named League One player of the month for August after scoring a hat-trick at Carlisle.
After starting his professional career with Rovers, he played for Swansea and Leeds before returning to Prenton Park permanently in 2011.
"Andy has been one of the first names on the team sheet since I returned to the club and I'm delighted he will be staying with us," said Tranmere manager Ronnie Moore.
"He's a great creative player with vision and awareness and as well as scoring goals he creates chances for his team-mates.
"There are not as many vocal players in the game as there used to be but Andy is a real presence on and off the pitch and someone who can help our younger players."