The mission involves five spacewalks to expand the ISS
Despite earlier concerns about poor weather, the shuttle blasted off at 1138 local time (1638 BST).
Its seven-strong crew will install the "Harmony" node to the space station.
The connecting unit will provide a passageway to the European Columbus laboratory, which is set to be fitted to the orbiting outpost in December.
Harmony has been built in Italy and its installation will be led by Italian astronaut and mission specialist Paolo Nespoli.
Shuttle flight STS-120, commanded by American Pam Melroy, will also allow a change of crew at the ISS.
Astronaut Daniel Tani will replace the long-stay resident Clayton Anderson, who has spent nearly five months living on the orbiting platform.
Nasa launch officials gave the go-ahead for the launch after damage was discovered on three wing-panels during an inspection at the weekend.
Engineers uncovered what was suspected to be cracks underneath the panels' protective coating. However, senior managers said that they did not believe repairs were necessary.
Weather conditions were also a concern on Monday evening. Nasa's weather officer warned that there was a 60% chance conditions would not be favourable for a launch.
Early on Tuesday morning, however, the risk from low clouds and sea breezes subsided, allowing the countdown to continue.
As well as the installation of Harmony, the flight will see the transfer of the first set of solar arrays placed on the ISS to a new permanent location.
Over the course of the two-week mission, five spacewalks will be needed to complete the programme of works.
Harmony will be the first expansion of the living and working space on the station since 2001.
Harmony will connect Europe's Columbus lab to the space station
It will provide a passageway between three science laboratories: the existing US Destiny lab; the European Space Agency's (Esa) Columbus module; and the Japanese Kibo experimental units.
It will also act as a docking port for the future Japanese re-supply vessels, the HTVs, and other shuttle missions.
Built by Thales Alenia Space, Harmony weighs some 14 tonnes. It is seven metres long and 4.6m wide.
Its launch marks the start of a busy few months for Esa at the ISS. The Columbus laboratory is set to fly to the platform in December.
And then in January, the "Jules Verne" Automated Transfer Vehicle (ATV) will launch from Kourou in French Guiana on a re-supply mission.
The ATV can carry 7.5 tonnes of equipment, food, fuel, air and other items to the orbiting outpost.
It will be the biggest and most sophisticated spacecraft Europe has ever lofted into space. The ship has an advanced navigation and docking system that enables it to find its own way to the ISS.
When the US retires the shuttle in 2010, the ATV will be the main means of supplying the station.
O lançamento do STS-120
Insignia da missão
O ônibus espacial Discovery foi lançado com sucesso esta manhã a partir do Complexo de Lançamento 39A no ''Kennedy Space Center'' em 11 e 38 EDT (UTC - 4).

Durante as duas semanas de missão, o ônibus vai entregar o Harmony Módulo para a Estação Espacial Internacional, bem como a preparação da estação espacial para futuras adições.

Cerca de duas horas antes do lançamento programado, A NASA descobriu e avaliou a ameaça representada por um quarto de 1,5 polegadas (3,81 - 10,16 por centímetros) de pedaços de gelo que tinha formado em um tubo que liga o tanque externo e O vaivém espacial motores principais. A greve de detritos no lançamento foi responsável pela perda do ônibus espacial Columbia, em fevereiro de 2003.