Mr Samuel is currently chairman at the Ecclesiastical Insurance Group and chairman of Howden Joinery Group, the remnants of furniture company MFI.
His CV includes spells as director of asset managerSchroders, a vice chairman of investment banking at Citigroup Europe, a senior adviser at investment bank Lazard and a senior adviser to the Prudential Regulatory Authority.
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He will join the TSB Bank board immediately.
Mr Samuel said: "The bank has an exciting future ahead as we move to independence and establish ourselves as the home of local banking."
TSB was launched as a high-street brand in September after being created from Lloyds's Verde portfolio, which it had tried to sell to the Co-operative Bank.
Lloyds must dispose of the Verde business, including the 189 branches of Lloyds TSB Scotland, as a condition of its 2008 taxpayer bail-out.
TSB, Britain's eighth-biggest high street bank with 631 branches, will be floated on the stock market this summer, although it is unknown whether Lloyds will dispose of its entire interest in the bank at the time.
Chief executive Paul Pester is keen to focus on TSB's support for local businesses and individuals, with named branch managers, the provision of unused branch space to local firms, and a local economy index to show where savers' deposits are being lent.
This harks back to the founding of the Trustee Savings Bank movement in Scotland more than 200 years ago when the Reverend Henry Duncan created a "bank for hard-working local people".
Lloyds chairman Sir Winfried Bischoff said: "This is a great appointment for Lloyds and for TSB.
"Will brings a wealth of experience to the role and is well regarded by the market and across the financial services industry.
"He is a key hire and will be instrumental in building TSB's independent future as a challenger to the other high street banks."