The first wave was expected to hit the Big Island by 11:19 a.m. local time, 4:19 p.m. ET, but that time has passed without unusually large wave activity measured along Hawaii's shores.
Hawaii Gov. Linda Lingle had said waves as high as 7½ feet could strike the Hilo area on the Big Island but much smaller 1½-foot waves are expected in Honolulu Harbor on Oahu.
Civil defense sirens blared in each county of Hawaii starting at 6 a.m. Hawaiian time as residents and tourists calmly began leaving their coastline homes and resorts and moving to higher ground. It was the first widespread evacuation for a tsunami in 16 years.
"The most important thing you could do is heed the instructions of state and local officials," President Obama, a Hawaii native, advised citizens in a statement today outside the White House.
"There is a tsunami in the water, in the Pacific, headed our way," said Nathan Becker with the Pacific Tsunami Warning Center.
Becker warned Hawaiians that the waves could be "going on for hours through the afternoon."
Red Cross officials are urging people to gather food and supplies to remain self-sufficient for at least three days.
Grocery stores faced a crush of residents eager to stock up on food, water and batteries. Long lines of cars snaked through many islands' streets near gas stations as drivers filled their tanks.
"We've got a lot of things going for us," Charles McCreery, director of the center, told The Associated Press. "We have a reasonable lead time. The evacuation should all take place during daylight hours, and wave impact should be during daylight hours."
Jayson Lum Kalani, a resident of Oahu, told ABCNews.com he was awakened by the sounds of the sirens blaring early in the morning.
"I thought it was a work crew," he said, noting that the sirens usually sound off the first day of each month as part of an emergency test system.
Kalani said he was not nervous about the pending tsunami on Oahu but had heard from friends on the Big Island who had evacuated. "It depends on what side of the island you are on [on the Big Island]," he said. "Hilo is more in the [tsunami's] path."
As a precautionary measure, the U.S. Navy has ordered four ships to leave the port of Pearl Harbor and remain at sea, where they will escape the crush of incoming water that could thrust them against the shore.
"This is a serious event," said Hawaiian Sen. Daniel Inouye. "If you live in the evacuation zone, I urge you to gather your family and please leave the area."
Tsunami Experts Call for 'Urgent Action'
The PTWC warning advises "urgent action should be taken to protect lives and property."
An estimated 40,000 to 50,000 people are in the affected areas of the Big Island and are said to be evacuating.
Emergency workers have begun going door to door urging people to heed the sirens, and homeless people who live on the beaches are being transported away in buses.
Buck Giles, a dispatcher with the Ocean Safety and Lifeguard Services Division for the City and County of Honolulu, told ABC News about 500 homeless people who live on the beach on the west side of Oahu are being taken from higher ground.
Roadblocks have been set up to prevent beach access, and along Waikiki, one of Hawaii's most famous beaches, guests in lower floors of the hotels are being told to move to higher floors.
The National Weather Service has reported that waves at Marquesas Island on the northern edge of French Polynesia, hundreds of miles south of Hawaii, were smaller than forecast, saying in a tweet "Hawaii impact could be less than initial expectations."
Six-foot tsunami waves were reported on some parts of French Polynesia. Those waves are expected to continue their northward motion.
Immediately following the 8.8-magnitude quake off central Chile, 4- to 8-foot waves were reported along the South American coastline.
"What we're looking at is a tsunami that could be two to three meters for some areas in Hawaii," Jenifer Rhoades, Tsunami Program Manager at the National Weather Service, told MSNBC. "That means it could be 6 to 8 feet of inundation in some areas."
The Federal Aviation Administration has closed Hilo International Airport on the low-lying eastern side of Hawaii's Big Island. Honolulu International Airport on Oahu is expected to remain open.
White House Monitoring Situation in Obama's Home State
White House press secretary Robert Gibbs said President Obama would be receiving updates during the day in the White House Situation Room.
The president made a statement outside the White House this afternoon, offering his condolences to victims of the Chile quake and assurances that the administration is making preparations for the tsunami.
"We can't control nature, but we can and must be prepared for a disaster if and when it strikes," Obama said.
The Federal Emergency Management Agency says it has "pre-deployed assets" in Hawaii, including food, water, generators and other resources ready to roll out as needed.
In addition to Hawaii, the tsunami warning also affects Guam, American Samoa and coastal areas of California and Alaska. The PTWC forecasts waves of 2 to 3 feet to could surge on the California beaches of La Jolla, Santa Monica, Los Angeles and Morro Bay.
Since a tsunami is a series of waves, emergency management officials are warning people to remain on alert even after the first wave or waves arrive.
"The time from one tsunami wave to the next can be five minutes to an hour," the PTWC bulletin reads. "The threat can continue for many hours as multiple waves arrive."
Residents are advised to remain on high ground until local authorities give the "all clear," which could come no sooner than two hours after the estimated time of the tsunami's arrival.
For ships and animals at sea -- including humpback whales that migrate to the Hawaiian Islands this time of year -- the tsunami poses little threat, experts say. The danger is as the surging waves come into shallow water, and have nowhere to go but up onto shorelines.
Following a 9.5-magnitude quake that struck Chile in 1960, the ensuing tsunami killed more than 200 people, including 61 in Hawaii.
Experts say any tsunami to hit Hawaii this time will likely be much smaller since the quake itself was not as strong.
ABC News' David Herndon, Jake Tapper, Luis Martinez and Nancy Ayala contributed to this report along with The Associated Press and Hawaiian ABC affiliate KITV.