The mission had suffered a slew of delays that kept the craft on the ground for weeks longer than planned.
Weather scrubbed launches Saturday, Sunday and Monday while technical glitches forced two postponements last month after technicians detected hydrogen gas leaks during fuelling just hours before the scheduled liftoffs.
Endeavour, which was expected to dock at the space station Saturday, is bringing a new resident to the station's crew, US astronaut Tim Kopra, to replace Japanese astronaut Koichi Wakata on the recently expanded six-person station crew.
Five spacewalks are planned for the 17-day mission with the installation of new space-station components and the delivery of spare parts, which are to help keep the station running after the shuttle programme is retired next year.
The 4,082-kg porch, known as the Japanese Experiment Module - Exposed Facility, is to be installed in the first spacewalk.