The agreement will allow face-to-face fundraisers to carry out up to 11 events a week, spread across three different areas of the city.
It comes two years after the council's city centre management department tried unsuccessfully to take legal action against a professional fundraising agency over its face-to-face activities.
John Ebo, deputy city centre manager at the council, said the legal route had not worked. The latest move was not a change of heart but a case of finding a solution that would work without creating problems, he said: "This agreement allows the activity to take place, but in a sensible and manageable way.
"People must be able to give if they want to, but there have also been far too many people collecting in the city."
Mick Aldridge, chief executive of the PFRA, said he appreciated the "pragmatism and far-sightedness" shown by Leeds city centre management.
The move comes as the Association of Town Centre Managers puts the final touches to a guidance paper for its members on how they should work with the PFRA.