The £600 million deal has an "initial" agreement lasting 10 years.
The agreement sees around 2,800 Tesco Bank employees working on banking products transferring to Barclays. According to Tesco Bank's key facts page, 3,540 people currently work for their banking wing.
Under the partnership there will continue to be Tesco-branded banking products and services and Tesco will receive an annual income for the use of its brand.
In Tesco's announcement, they stated the deal removes £7.7 billion of capital-intensive assets and £6.7 billion of financial liabilities from their balance sheet.
In addition to the £600 million, the supermarket expects to see a further £100 million in net cash after the settlement of certain regulatory capital amounts and after transaction costs.
Tesco will retain all other existing activities of their banking wing, including insurance, ATMs, travel money and gift cards.
The agreement is conditional on court sanction and regulatory approval or non-objection, with completion expected in the second half of 2024.
The supermarket bank was previously reported to have been mulling the sale early last year.
Ken Murphy, Tesco group chief executive said: "The transaction will also significantly reduce our financial liabilities, in turn strengthening our balance sheet and allowing us to focus on continuing to grow our core retail business. I’m hugely grateful to our colleagues for their dedication and excellent service to our customers, and I’m confident that this new partnership approach will build on that success.”
Coimbatore Sundararajan Venkatakrishnan, Barclays group chief executive added: "We are looking forward to working closely with the team at Tesco over the coming months to enable a smooth transition and, subject to completion of the transaction, we look forward to welcoming Tesco Bank colleagues and customers to Barclays.”