The Lloyds said the move was part of a push to develop better digital services for customers with insurance, pensions and investment products.
"The new platform will make managing heritage products simpler and more efficient for LBG customers," Lloyds said in a statement, adding that "staff will be able discuss the non- contractual arrangements with Diligenta over coming months".
The move, which affects staff based in the Bristol and Edinburgh offices of Lloyds' Scottish Widows and Clerical Medical divisions, has come under criticism from workers' unions.
"The wholescale transfer of 1,000 Lloyds Banking Group staff to Diligenta is nothing short of a betrayal of these workers," said Rob MacGregor, national officer at Unite union.
"The bank's 'sale' of its committed Scottish Widows and Clerical Medical staff represents contempt for long serving and skilled employees," he said.
The union fears the transfer will affect staff pension benefits and other non-contractual Lloyds perks once they join Diligenta at existing offices under a Transferof Undertakings (Protection of Employment) arrangement.
MacGregor added, "Unite is calling on Lloyds to reconsider this shameful deal and do the right thing by its staff who have worked hard to ensure the business is the success it is today."
"The message from the Lloyds Banking Group is loud and clear and appears to be 'so long, thanks for your efforts, you work for them now'," he said.
A Scottish Widows spokesperson said: "Lloyds Banking Group has partnered with Diligenta to enhance its service proposition for customers with heritage life, pensions and investment products through a new digital platform."
"Diligenta already successfully manages more than 11 million life and pension policies in the UK on its end-to-end policy administration platform."
The Lloyds had returned to private ownership in May after the UK government sold the last of its stake in the bank.
The latest outsourcing move will fan speculation over the future of its Scottish Widows business and that the bank may be interested in selling the insurance division to Standard Life.
TCS subsidiary Diligenta describes itself as a transformational business process services provider, with an approach to simplify inherited operations, business processes and IT architecture through transformation.
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