The move comes after years of turmoil for the company, which once symbolised Japan's economic might but more recently has been mired in scandals, financial turmoil and resignations.
The Japan Industrial Partners-led consortium taking control in the nearly two trillion yen deal includes 17 Japanese firms and six Japanese banks.
In March, Toshiba said the tender offer will be called off if the consortium fails to buy at least 66.7 percent of the outstanding shares.
The price is set at 4,620 yen per share and the period 30 business days, according to the website on the tender offer, slightly higher than Monday's closing price of 4,584 yen.
Toshiba on Monday reported a net loss of 25.3 billion yen for the first quarter because of a drop in demand at chip firm Kioxia, in which it retains a 40 percent stake.
Two years ago, a bombshell buyout offer from private equity fund CVC Capital Partners put a question mark over the conglomerate's future.
After the CVC offer was dropped, plans were floated to split the company up and spin off its device segment -- meeting stiff opposition from some investors.
Toshiba grew into a vast conglomerate, but has been in upheaval since it was rocked by a profit-padding scandal in 2015.
The company also suffered from huge losses at its US nuclear subsidiary, followed by a recovery that brought pressure from new activist shareholders.
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