The orbiter and its five astronauts will deliver and install a pair of giant solar wings on the space platform. The huge solar panels will shine in the night sky when unfurled.
"People will be able to look up and see the brightest new star in the sky," said Nasa space development administrator Michael Hawes.
The $600m panels will be folded for launch. But once they are deployed on the ISS, this first set of solar panels will measure 73 metres (240 feet) tip-to-tip, providing enough electricity to run 15 average-sized homes.
"This mission will assemble the heaviest, largest and most complex piece of the International Space Station to date," Ron Dittemore, the space shuttle programme manager, said.
"Every shuttle flight for the next year carries its own set of firsts. But this mission, unfolding solar arrays of historic proportions, will make the challenge and grandeur of this entire venture more apparent than will any other single flight."
Endeavour is scheduled to lift off on Thursday at 2306 EST (0306 GMT Friday) from the Kennedy Space Center, Florida.
The launch window is only five minutes long but meteorologists are confident the weather at least will not cause a delay. There is a 90% probability of fair skies.
Veteran astronaut Brent Jett will command the mission. Michael Bloomfield will serve as pilot. They will be accompanied by Joe Tanner, Carlos Noriega and Canadian Space Agency astronaut Marc Garneau.
It will be Tanner and Noriega who will go outside the orbiter to help attach the giant solar panels to the station.
Once this has been achieved, there will be sufficient power for the station's three residents - Bill Shepherd, Yuri Gidzenko and Sergei Krikalev - to open a module that has been sealed since their arrival almost one month ago.
The extra power will also be used to operate the American Destiny lab when it is added to the growing station in January.
The orbiter crew and the station residents will not actually spend much time together during this mission. The hatches between the shuttle and ISS will not be opened until all three spacewalks are complete.
For a variety of reasons, air pressure is kept lower aboard the shuttle than on the station when astronauts are moving back and forth through airlocks. In the end, the two crews are scheduled to spend only about a day together, most of that spent stowing space-station rubbish on the shuttle for a return flight to Earth.