The lender currently owns 58.52% of L2D and its insurance arm Liberty Group will acquire the remaining shares from minority shareholders at R5.55, a more than 40% premium to Wednesday's closing price, the companies said in a statement.
The purchase of all the outstanding shares would cost Standard Bank around R1.87bn ($106m), according to Reuters calculations based on Refinitiv data.
Shares of L2D, which counts Johannesburg's Sandton City mall among its assets, jumped on Thursday to close in line with the offer price.
Most of South Africa's property companies, which operate as Real Estate Investment Trusts (REITs), are trading far below the value of their assets, sparking sector consolidation, buy outs and de-listings.
Shares have underperformed with the property index up 44% since a March 2020 crash, compared with banks and mining companies which have more than doubled in value.
"The macro-economic environment has resulted in a valuation deterioration across the listed property sector since 2018, exacerbated by the Covid-19 pandemic," L2D said.
L2D has stakes in 15 properties across the country with a value of R8.2bn, translating to R7.51 per share, 35% more than the offer price.
"If you believe the long term valuation is correct ... you are buying the assets at a discount, despite the big premium," said Wayne McCurrie, portfolio manager at lender FNB and a director of rival Emira Property Fund.
Casparus Treurnicht, portfolio manager at Gryphon Asset Management, said the lender was taking a long term view on the turnaround of the sector as interest rates ease in the future.
L2D will announce its interim results for the six-months ended 30 June on Monday. Its shares will be delisted after the tender.
($1 = 17.6281 rand)
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