The supermarket’s financial arm, Tesco Bank, will reward customers with one Clubcard point for every £4 they pay off their mortgage.
Rates for the mortgages, which require at least a 20% deposit, start from 3.19%.
However, analysts have questioned the competitiveness of the interest rates, with several big lenders already offering fixed-rate mortgages at under 3% interest.
Tesco, which already offers loans, credit cards and insurance, is the latest retailer to attempt to increase its share of the financial market.
Marks & Spencer laid out plans in June to open 50 in-store banking branches in the UK over the next two years under the new M&S Bank brand.
Last month Asda relaunched its personal finance offering under a new name, Asda Money, and added a “cash back” credit card to its motoring, life and travel insurance products.
Tesco chief executive Philip Clarke said: “Customers want choice in banking from a brand they know and trust to deal with them fairly. The launch of Tesco Bank mortgages is a major milestone towards offering Tesco customers a full retail banking service.”