A blue-eyed boy of the billionaire investor, Sokol's surprise exit has come amid disclosures about his personal stockholdings.
Expressing "surprise" over Sokol's stepping down, Buffett said that he had not asked for his resignation.
Sokol was chairman of several Berkshire Hathaway subsidiaries, including MidAmerican Holding Company.
His exit was announced by the 80-year-old Buffett in an "unusual" press release late Wednesday.
Buffett is the world's third richest man with fortunes worth $50 billion.
Sokol has left the group amid disclosures that he purchased shares of Lubrizol some days prior to the company's takeover deal with Berkshire Hathaway.
"Neither Dave (Sokol) nor I feel his Lubrizol purchases were in anyway unlawful. He has told me that they were not a factor in his decision to resign," Buffett said.
Earlier this year, Berkshire Hathaway agreed to acquire global chemical major Lubrizol in an over $9 billion deal.
Sokol was instrumental in initiating the transaction talks.
exit comes at a time when the corporate world is closely watching Buffett's succession plans.
Apart from Jain, who is heading Berkshire Hathaway's reinsurance business, two other possible contenders for the billionaire investor's mantle are Matthew Rose, head of Burlington Northern Santa Fe railroad, and Tony Nicely, a top executive at Geico property insurance business.
During his recent trip to India, Buffett not only showered praise on Jain but had also said that Berkshire Hathaway's board members would not have any issues in handing over the reins of the conglomerate to him.
On Wednesday, Buffett said that Sokol's resignation letter on March 28 was a "total surprise" despite the two earlier resignation talks.
"I had spoken with him the previous day about various operating matters and received no hint of his intention to resign. This time, however, I did not attempt to talk him out of his decision and accepted his resignation," Buffett noted.
According to the billionaire investor, Sokol had bought 2,300 Lubrizol shares on December 14, which was then sold on December 21.
"Subsequently, on January 5, 6 and 7, he bought 96,060 shares pursuant to a 100,000-share order he had placed with a $104 per share limit price," he noted.
Buffett came to know these things shortly before his trip to Asia (South Korea and India) on March 19.