The president writes that Chicago will provide a spectacular Olympic experience.
"The City of Chicago is designed to host global celebrations and it will deliver a spectacular Olympic experience for one and all," Obama said.
The 338-word typed form letter, dated Sept. 10, is addressed to individual members and bears the signature of the president. It raises the possibility of Obama going to Copenhagen to push the Chicago bid at the Oct. 2 vote.
Chicago -- seeking to host the Summer Olympics in the U.S. for the first time since 1996 -- is in a tight contest with Rio de Janeiro, Tokyo and Madrid.
"I deeply appreciate the tremendous work of the Olympic Movement and wish to convey my strong support for Chicago 2016," Obama said in the letter, citing the "transformative power" of the Olympics to unite people.
Obama, who served as a senator from Illinois and calls Chicago home, said he has supported the city's Olympic bid since it was launched in 2006.
"As President, I see the 2016 Olympic and Paralympic Games as an extraordinary opportunity for America to renew our bonds of friendship and welcome the world to our shores with open arms," he said. "If you honor Chicago with your selection, we will ensure that the Olympic and Paralympic Games are a key priority for our nation."
Obama noted that he has already established a White House office of Olympic and youth sport.
"You can count on our government to support Chicago's quest to host an unforgettable event and strengthen the Olympic movement," he said. "I believe we have an historic opportunity to do great things together, and I look forward to discussing that opportunity with you, if not in Copenhagen, then soon thereafter if Chicago is your choice."
The letter is dated a day before the White House announced that Obama was unable to commit to going to Copenhagen because of the health care debate, and that he was sending first lady Michelle Obama to lead the Chicago delegation.
Since then, the White House has left open the possibility that Obama will make a last-minute decision to join his wife in Copenhagen. An advance White House team has traveled to the Danish capital to make preparations for a possible presidential trip.
Brazilian President Luiz Inacio Lula da Silva and Spanish King Juan Carlos have said they will be in Copenhagen for the vote. Tokyo's bid organizers are urging new Prime Minister Yukio Hatoyama to attend.
The Associated Press contributed to this report.