Coventry Building Society said on Monday that it intended to appoint Mr Hoffman to the role, confirming the move first reported by Sky News.
The appointment is subject to regulatory approval and would see him joining the board on 26 April.
The building society said: “Mr Hoffman brings wide-ranging experience of financial services from a career that includes executive and non-executive positions in banking, insurance and payments services.”
Mr Hoffman will replace Peter Ayliffe, who has been acting as interim chairman since the death of Ian Pickering last autumn.
Born in Coventry, Mr Hoffman has retained strong links to the city, having tried on a previous occasion to lead a takeover of its League Two football club from Sisu Capital, its controversial hedge fund owner.
A City source said this weekend that Mr Hoffman had recently resigned from the board of Visa Inc, the New York-listed payments giant, in order to take up the Coventry Building Society role.
The Coventry, which had mortgage loans of almost £36bn at the end of last year, is the UK’s second-largest building society, behind only the Nationwide.
It reported pre-tax profits for 2017 of £243m and cemented its position as a top 10 UK mortgage and savings provider.
Mr Hoffman’s arrival, which one source described as “a major coup” for the mutual, will underline the scale of the Coventry’s ambitions under Mark Parsons, its chief executive.
After leaving Northern Rock, Mr Hoffman had a stint at the helm of NBNK Investments, a vehicle set up to acquire bank assets from lenders rescued by UK taxpayers.
NBNK was close to acquiring hundreds of branches from Lloyds Banking Group but lost out to the Co-op Group, which was ultimately forced to abandon the deal as it too teetered on the brink of collapse.
Mr Hoffman then became chief executive of Hastings, the motor insurer, steering it through its public listing before stepping up to become executive chairman earlier this year.
His appointment at the Coventry will come at a time of growing headwinds for building societies and other mortgage lenders? amid a softening of the UK housing market.