Previously vice-chair of the trade body for two years, Williams has been a member of its board since 2001. Like Neale, he will serve a two-year term after being selected by the PRCA board at the organisation's AGM yesterday.
The new vice-chair is Jim Donaldson, UK and Middle East CEO of FleishmanHillard Fishburn.
Williams was the founder of Publicis Groupe firm Capital MSL, which he ran for 12 years before joining Finsbury.
Williams said it was "an honour" to take on the role, and said a particular priority under his leadership would be to "make the PRCA even more visible in City and financial PR, a great strength of the PR industry, and of the UK economy alike".
Francis Ingham, director general of the PRCA, said: "The past two years working with Matt Neale have been an absolute pleasure. Under his leadership, the PRCA has grown enormously. We now represent and regulate more than 20,000 PR practitioners; we have a new base in the Middle East and North Africa; we have never hesitated to stand up for our industry."
The organisation will reveal its new name next week.