Donald Trump appointed Ms Murphy as the GSA Administrator in 2017. Two weeks after Mr Biden was declared the winner of the US election, Ms Murphy confirmed that the transition could begin.
By delaying the transition, Mr Biden’s team were blocked from accessing Government information and funding.
On Monday, a letter obtained by CNN showed that Ms Murphy has now allowed the transition to proceed.
However, she revealed in the letter that she had received threats urging her to let the transition process begin.
Ms Murphy also insisted she had not been pressured by the White House to delay the formal transition.
In the letter, Ms Murphy wrote: “To be clear, I did not receive any direction to delay my determination.
“I did, however, receive threats online, by phone, and by mail directed at my safety, my family, my staff, and even my pets in an effort to coerce me into making this determination prematurely.
“Even in the face of thousands of threats, I always remained committed to upholding the law.”
President Trump thanked Ms Murphy for her “dedication” and said he did not want her to be abused.
Writing on Twitter, Mr Trump said: “I want to thank Emily Murphy at GSA for her steadfast dedication and loyalty to our Country.
“She has been harassed, threatened, and abused – and I do not want to see this happen to her, her family, or employees of GSA.”
President Trump also insisted that he would continue to challenge the election result.
He wrote: “Our case STRONGLY continues, we will keep up the good fight.
“And I believe we will prevail! Nevertheless, in the best interest of our Country, I am recommending that Emily and her team do what needs to be done with regard to initial protocols, and have told my team to do the same.”
Analysts have called the letter “as near as we’ve had to a concession” from President Trump’s team.
So far President Trump has refused to accept Mr Biden’s election victory.
Ms Murphy said she will open up resources for Biden’s team to allow the transition to formally begin.
In the letter, she wrote: “I take this role seriously and, because of recent developments involving legal challenges and certifications of election results, am transmitting this letter today to make those resources and services available to you.
“I have dedicated much of my adult life to public service, and I have always strived to do what is right.
“Please know that I came to my decision independently, based on the law and available facts.
“I was never directly or indirectly pressured by any Executive Branch official – including those who work at the White House or GSA – with regard to the substance or timing of my decision.”
Mr Biden’s team welcomed the decision to allow the transition to begin.