Gilbert, who starts at the bank on 2 December, is key projects director for Virgin Management and was previously chief marketing officer at Virgin Media.
He has worked for Lloyds before as group marketing director of Lloyds Banking Group between 2008 and 2012, contending both with the credit crunch and the bank's sponsorship of the London 2012 Olympic Games.
TSB was recreated as a working bank brand in order for the group to satisfy the European Commission's requirement that it sell off hundreds of branches in punishment for taking a state-funded bailout in 2008.
The brand was formally launched in September with around 5 million customers transferred from Lloyds TSB, which has since renamed itself Lloyds Bank.
TSB is still owned by Lloyds but is set for an IPO next year to complete the required separation.
Gilbert will report to TSB chief executive Paul Pester, who was formerly MD of consumer banking and payments for Lloyds Banking Group.
Pester said: "Having worked with Nigel before, I’m confident that his breadth of experience across brand, customer experience, communications and corporate affairs will be instrumental in delivering our TSB brand strategy now and over the coming years."
In a statement about his new role, Nigel Gilbert slid in a reference to TSB's 'Welcome back to local banking' launch slogan.
"The launch of TSB earlier in the year represented a significant moment for banking. TSB understands the value of placing local communities at the heart of everything it does and I am looking forward to welcoming customers, old and new, back to local banking."