Bradley, a former managing partner at rival City firm Brunswick, is expected to join Finsbury after almost four years at Tulchan.
The move comes in the week that Brunswick had its annual meeting of partners, this year in China.
It is understood that one of the items on the agenda was changes to the equity make-up of the business, with a view to incentivising Brunswick's 80 partners to stay at the firm.
One source said: 'Brunswick has long had an issue in that equity is very tightly held and some partners feel they are building the business for the benefit of others.'
There is no suggestion that Brunswick boss Alan Parker is relinquishing control, but Brunswick is understood to be reviewing ways to enable partners to increase their equity holdings.
It is understood that Parker retains a controlling share in the business, while the agency's partners are primarily incentivised through performance-related bonuses rather than equity.
Brunswick declined to comment.
Meanwhile Bradley is understood to be leaving Tulchan at the end of this week and is expected to join his new agency after a period of gardening leave.
Tulchan hired Bradley after 20 years with Brunswick in 2007, enticing him with a package understood to include an attractive equity stake in the independent City shop and a guaranteed bonus.
The firm changed from a limited company to an LLP structure recently and a number of top City PR sources suggested that changes to the partnership agreement may have played a part in Bradley's departure.
Tulchan insiders played down this suggestion, but agency founder Andrew Grant declined to comment on the reasons for Bradley's departure.
Opportunities for senior City staff to take significant equity in agencies are limited as only a handful of financial PR agencies remain independent and there have been few recent start-ups of any scale.