Hewlett-Packard is expected to combine its computer and printing businesses, with the San Diego-based head of its printing arm, Vyomesh Joshi, leaving the company as a result.

AllThingsD, a technology website affiliated with The Wall Street Journal, reported Tuesday that Palo Alto-based HP will announce the combination of its personal computer and printer businesses shortly. The report cited unnamed sources familiar with the matter. Bloomberg News also reported the move, saying HP aimed to cut costs and simplify operations.

Both news organizations said Todd Bradley, who now oversees HP’s Personal Systems Group, would run the combined division and Joshi would leave the company.

Merging the two giant divisions would be the first major turnaround move taken by new CEO Meg Whitman, the former eBay head who signed on at HP in September.

Joshi, 57, has been with HP for 32 years — all of them based out of the company’s inkjet product development facility in Rancho Bernardo.

A popular executive known as VJ, he worked his way up the ranks, eventually becoming head of HP’s $26 billion Imaging & Printing Group in 2001.

The printing division was HP’s top financial performer for years, helping the company weather struggles in other business units — particularly the computer division — following HP’s acquisition of Compaq in 2002.

“VJ has always been a rock-steady influence on that company,” said Gary Peterson, chief executive of Gap Intelligence, an industry research firm. “He helped carry HP through some very difficult times, and it will be hard for someone to fill those shoes.”

Growth in the printing business has slowed recently. Revenue was flat at $25.78 billion and operating profit down 9.9 percent to $3.973 billion for HP’s 2011 fiscal year.

The company blamed supply issues linked to the earthquake and tsunami in Japan, as well as unfavorable foreign currency rates.

HP’s personal computer division had mixed results in 2011. Sales fell 2 percent to $39.95 billion but operating profit rose 15 percent to $2.35 billion compared with the prior year.

There was no response to a phone call to Joshi’s office on Tuesday. In an interview in October, Joshi spoke enthusiastically about the long-term growth potential for printing.

“You think with everything going digital, everyone would be reading electronically. Why would people even care about printing?” Joshi said at the time. “But we think there is a big opportunity.”

He acknowledged that people are consuming more content on wireless phones, tablets and computers that is never printed. But he also said that because digital content is so easy to create there’s exponentially more of it available, especially online. And that means there’s more out there to potentially print.

Joshi focused on connecting printers to the Web directly without relying on computers. HP’s Web-connected printers have their own email addresses. People can print from their wireless phones, tablets or laptops simply by sending an email to their Web-connected printer. Joshi also pushed HP deeper into the commercial printing business with new digital presses for newspapers, book publishers and other firms that still print using analog presses.

HP’s giant WebPress — a bus-size inkjet printer developed in San Diego — can customize pages on the fly and reduce waste by allowing commercial printers to economically produce fewer copies in each press run.

When Carly Fiorina was fired as HP’s chief executive officer in 2005, Joshi’s name emerged as a possible replacement. The job ultimately went to ex-NCR chief Mark Hurd, who was dismissed by the company’s board in 2010.

Hurd was replaced by Leo Apotheker. But HP’s board let Apotheker go after just 11 months following a controversial proposal to spin off the computer business, and replaced him with Whitman.

Besides running HP’s printing business, Joshi also sits on the board of Yahoo. Peterson thinks Joshi will have job offers if he indeed leaves HP. “He could be the CEO of a major tech company if he wanted to be,” Peterson said.