Baroness Morgan takes on a crucial Downing Street role
Tony Blair appointed the peer following the announcement on Thursday of Ms Hunter's departure to oil giant BP.
Lady Sally Morgan has served as Cabinet Office minister with responsibility for women's issues since the June general election, before which she was Mr Blair's political secretary
Her move to the Lords in Mr Blair's post-election reshuffle, while Ms Hunter remained at Downing Street on an increased salary with wider responsibilities, was seen as confirmation that Lady Morgan had lost a long-running turf battle with Mr Blair's friend from school days.
Ms Hunter's moving on from Number 10 now allows Lady Morgan to take over her rival's old job.
'Enormous regard'
A spokesman said Mr Blair had "enormous regard" for Lady Morgan.
"She is an extremely talented individual, has excellent judgment and is well known as someone who has worked extremely closely with the prime minister in the past."
Ms Hunter has been one of Mr Blair's closest and most trusted aides since long before he became Labour leader in 1994, and had long acted as his "door keeper".
She joins BP as its director of communications in the new year, with Mr Blair wishing her "every success" in the job.
In a statement the prime minister said: "Anji has made a fantastic contribution to government and the Labour Party,"
"Our loss will be BP's gain."
Ms Hunter had been expected to leave Downing Street during this parliament and began talking to BP privately about a job before the general election.