The 23-year-old was given permission to speak to the League One club by the Daggers but passed on the chance to move to London Road.
A statement on Dagenham's website read: "On Sunday the Board of Dagenham & Redbridge FC reluctantly gave permission to Peterborough United FC for them to speak to Rhys Murphy with a view of transferring his registration to them.
"After various discussions by all parties it has become clear that Rhys does not wish to make such a move at this time and is more than happy to commit his playing future to the Daggers for the foreseeable future."
Manager Wayne Burnett was thrilled to keep his top scorer at the club.
He said: "I'm absolutely delighted that Rhys Murphy has decided to stay at our football club, you never want to lose key players. He's an integral part of what we have done so far this season."
Former Arsenal trainee Murphy has scored 12 goals for Burnett's side this season.