The American, who burst from the pack to win by three shots after a sizzling last round of 66, climbed above Northern Ireland's Rory McIlroy into second place in the rankings behind Tiger Woods who is still comfortably ahead.
Mickelson has never topped the official world rankings which were brought in 24 years ago.
The 43-year-old's charge to his first British Open title proved a popular one amongst his fellow professionals with the left-hander receiving widespread praise.
His swing coach Butch Harmon said his performance on Sunday in the wind and with difficult pin positions was the best he had ever seen.
"I said when Greg (Norman) won in 1993 that was the best round of golf I'd seen, but I think this one tops it," Harmon told the BBC. "He just embraced how to play on a links course."
Justin Rose, who beat Mickelson to the U.S. Open title this year, said on Twitter: "Really pleased for Phil. I feel good for him especially after all the courtesy and sportsmanship he showed me at the Ryder Cup and U.S. Open."
Mickelson's long-time caddie Jim "Bones" Mackay, who was tearful afterwards, said winning the British Open ranked alongside the American's three Masters triumphs.
"I think it ranks right up there among his previous wins, Mackay said. "I love the Masters but I love the British Open, especially in Scotland. It means the world for me as his caddie at least, to win - it's very special."