The bank said it will cater to the needs of Britain's approximately 1.8 million Muslims, following in the footsteps of the Islamic Bank of Britain (IBB), which opened in London last September offering the same service.
The service differs from conventional British mortgages because it is "based on completely different principles", said Lloyds TSB's Emile Abu Shakra on Monday.
"What we are doing is buying the property on behalf of the customer and then leasing it back to them in a way which allows them to legally own it at the same time, to get ownership."
Crucially, no interest will be payable, because under Islamic law both payment and receipt of interest are forbidden.
However, the amount paid over the 25-year term will be broadly similar to a conventional mortgage.
Under the new mortgage, the bank will fund up to 90% of a house purchase and the customer will then repay that sum over a fixed period, alongside a rent payment for use of the property.
"It's a form of rental, but it's completely compliant with Islamic law and avoids the interest system so it looks the same," Abu-Shakra added.
The mortgage offers a solution to Muslim customers who want to buy a property but who will not enter into a traditional mortgage agreement, the bank said.
"With traditional, interest-based mortgages out of the question for many [Muslims], the choice has tended to be between going against the faith or avoiding a mortgage altogether"
"Finding the money for a new home can be tough at the best of times, but Britain's Muslims face an even more difficult dilemma," said Mark Austin, of Lloyds TSB Islamic Financial Services.
"With traditional, interest-based mortgages out of the question for many, the choice has tended to be between going against the faith or avoiding a mortgage altogether."
The move follows Lloyds TSB's recently-launched Islamic bank account, which also offers no interest or overdraft facilities to comply with Sharia law.
Muslim financial products
The mortgage and current account are being piloted in branches across heavily-Muslim populated areas of Britain, including Edgware Road in central London, Luton, north of the capital, and the country's second city Birmingham.
Both services can be operated through any of the bank's 2000 branches across Britain.
The market for Muslim-orientated financial products is a growth area for the bank, it said.
"The Muslim population in the UK is one of the fastest-growing communities," Abu-Shakra said.
"There are around two million Muslims in the UK at the moment, they haven't had access to this type of product in this way before so, it's going to be attractive to them. There is definitely a market for it."