Benchmark agreed to drop the lawsuit in return for Kalanick's board power being diluted but its co-operation depends on the Softbank investment going through.
Under the terms of the deal, it is understood that Softbank will lead a $1 billion funding round with participation of Dragoneer Investment Group, a San Francisco-based investor.
Softbank would buy $1 billion in new stock and purchase shares from investors and employees worth up to 14 percent of the ride-hailing company.
Uber Technologies Inc. confirmed the investment in a statement Sunday without giving details.
Disagreements in the tech firm's board appear to have been resolved, as early investor Benchmark Capital had been adamant that former CEO Travis Kalanick step down and withdraw his influence from the company.
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Softbank is reportedly investing at a valuation of around $68 billion, while the purchase of existing shares will be done...
"We believe this agreement is a strong vote of confidence in Uber's long-term potential", it said. Both sides ended their feud on Sunday, clearing the way for the SoftBank investment, the person said. But there will likely be heavy arguments about the shares' worth in the coming weeks. Kalanick is agreeing to give Uber's board majority approval over the board seats he controls should he ever need to fill them again, the people said.
The two parties have now reached an agreement on control of board seats, which included Benchmark putting its lawsuit on hold - while Kalanick will allow directors to vote on his future appointments to the three seats he oversees, the Wall Street Journal reported, citing anonymous sources.
SoftBank is sending tremors through the tech world with its massive new Vision Fund, a venture capital fund intended for startups and expected to dominate the industry before long.
Completing the SoftBank deal would allow Uber to open a new chapter after a year of controversy, including the resignation of Kalanick, the ouster of several top executives, sexual harassment and discrimination allegations, and multiple federal criminal probes. The company has threatened to invest in ride-hailing rival Lyft if it does not get the Uber deal done.