TOKYO — Sony is set to become the biggest shareholder in Olympus with an investment of 50 billion yen, or $645 million, investment, the two companies announced Friday.

The deal could give struggling Sony a jump-start in the lucrative medical equipment business, while helping to bolster Olympus’s balance sheet following its $1.7 billion accounting scandal.

Sony and Olympus will form a joint venture to develop and manufacture endoscopes and other medical devices, the companies said in a statement. Olympus controls about 70 percent of the world’s market for medical endoscopes.

The two companies will also consider cooperating in digital cameras, they said.

Sony, struggling after four years of losses because of its slumping TV business, has been looking for new sources of revenue. It entered the medical device field last year by acquiring the American medical diagnostics firm Micronics for an undisclosed sum. Sony’s president, Kazuo Hirai, has said medical businesses could one day be a major profit driver.

Meanwhile, Olympus, which admitted last year to hiding losses for over a decade, is desperate to shore up its capital.

It replaced its entire board, restated five years of earnings and took a $1.3 billion write-down after acknowledging that it obscured what it said were past investment losses in inflated mergers and acquisition payments.

The deal announced on Friday calls for Sony to take a 11.5 percent stake in Olympus by buying new Olympus shares for 1,454 yen a share — a 4 percent discount to Friday’s closing price.

The two companies will set up a joint company by the end of the year, of which Sony will hold 51 percent and Olympus will hold 49 percent, the companies said. Sony will also select a director to serve on Olympus’s board.

In statements, Hiroyuki Sasa, the Olympus president, and Mr. Hirai of Sony both stressed that the deal would bring together Sony’s technological edge in digital imaging with Olympus’s already-dominant position in the medical field.

‘‘By accepting an investment from Sony, we will not only strengthen our financial base, but also combine our strengths and develop the kind of medical devices that we may not have been able to develop on our own,‘‘ Mr. Sasa said.

Sony will position the medical field ‘‘as one of Sony’s future core businesses,’’ Mr. Hirai said.

Olympus shares gained 1.7 percent to 1,520 yen in Tokyo on Friday, after the Nikkei business daily carried a report on the deal in its morning edition. Shares in the company, which lost nine-tenths of their value after the scandal erupted last October, have recovered to almost half their pre-scandal levels.

Shares in Sony fell 1.1 percent to 919 yen. Its shares have already slumped 34 percent this year.

On Tuesday, Standard & Poor’s cut Sony’s long-term debt rating a notch to BBB, the second-lowest investment grade, and warned of further downgrades unless Sony turns its business around.