"We therefore congratulate Michael Dell and I intend to call him to wish him good luck (he may need it)," Icahn wrote in the letter.
Michael Dell's $24.8 billion bid to take his company private includes an offer of $13.75 per share plus a 13-cent dividend. Dell raised that bid last month after previous offers also drew strong criticism from Icahn and other major Dell Inc. investors.
Dell's shares have plunged by more than 40 percent since Michael Dell returned for a second stint as CEO in 2007, largely because the company has had trouble adapting to a technological shift that has caused PC sales to fall as more people use smartphones and tablets.
The company said last month that its fiscal second-quarter earnings fell 72 percent, in part because of price-cutting aimed at slowing a sales decline.
Michael Dell wants to take his company private and diversify. He foresees the business going through a painful transition that will likely hurt earnings, something that will be easier to endure without Wall Street's fixation on short-term results.
But Icahn has said the buyout would keep stockholders from sharing gains the company will reap from an eventual turnaround. His announcement Monday comes more than a month after he vowed to keep fighting Michael Dell's bid and said "the war regarding Dell is far from over."
Icahn wanted to oust Dell's board and pursue a complex alternative to Michael Dell's bid that Icahn has said would be worth at least $15.50 per share. He has said that if his board candidates were elected, he could guarantee that Michael Dell would no longer be CEO.
Icahn told CNBC Monday afternoon that he was close to getting a "top name" he declined to identify to serve as CEO.
Ultimately, though, Icahn told fellow investors that a Delaware court ruling and the higher bid from Michael Dell and Silver Lake Partners — they had raised the offer from $13.65 per share and added the dividend — hurt his chances in Thursday's vote.
Icahn wanted the vote on Michael Dell's offer and the company's annual meeting to be scheduled the same day so he could oust the board. But he noted in his shareholder letter that a Delaware judge ruled that the gap between Thursday's vote and the annual meeting set for next month was legal.
The investor said he believed that combining those meetings would have pressured Michael Dell and Silver Lake to raise his offer even more.
Icahn also had complained that Dell's directors unfairly favored Michael Dell by moving up the investment date that makes a shareholder eligible to vote and by counting only votes that were actually cast, excluding those controlled by Michael Dell's group.
Dell's board moved up the cutoff date for voting eligibility to Aug. 13 from June 3. The created a new pool of voters, including many investors who bought the stock in the past few months and stand to profit from the sweetened offer.
The vote on Michael Dell's buyout offer had already been delayed a few times as Michael Dell's group tried to rally support. That prompted Icahn to compare the company to a dictatorship.
"We jokingly ask, 'What's the difference between Dell and a dictatorship?," he said in his shareholder letter. "The answer: Most functioning dictatorships only need to postpone the vote once to win."