Atlantis was supposed to blast off on Thursday, but delays to the launch of an Atlas III rocket from Cape Canaveral, also because of poor weather, meant the ISS mission had to wait a day.
Lift-off, originally scheduled for 13 April, was knocked back because of poor weather.
But with the weather finally on its side on Friday, Nasa succeeded on its fourth attempt to launch the shuttle at 06:12 local time (10:12 GMT) at Cape Canaveral, Florida.
"We're on our way to the station," called out shuttle commander James Halsell Jr.
Orbit boost
The shuttle is expected to dock with the ISS early on Sunday.
Atlantis was supposed to blast off on Thursday, but delays to the launch of an Atlas III rocket from Cape Canaveral, also because of poor weather, meant the ISS mission had to wait a day.
The $60bn ISS could not have waited much longer for a visit from Earth. Building work on the station has fallen behind schedule. The orbiting platform also requires repairs to elements already constructed.
The Atlantis crew will have to replace four of six solar-charged batteries that are malfunctioning, and use the shuttle's engines to boost the station's falling orbit.
It is dropping by about 2.4 kilometres (1.5 miles) a week. The station's current height is about 340 km. Atlantis will push it up a further 40 km during the six days that the spacecraft are docked.
The crew will also try to buffer noise inside one of the two existing modules. At 75 decibels, noise is about as loud as heavy traffic and doctors worry that long-duration crews could suffer some deafness from prolonged exposure.
Broken antenna
Spacewalking astronauts will put the finishing touches to a Russian construction crane outside the ISS and will also try to repair a broken communications antenna.
Finally, the crew of six Americans and one Russian will take multiple on-board air samples to help scientists on the Earth learn why an earlier supply crew got sick while working there.
Atlantis will be carrying an Olympic 2000 torch, unlit of course, and an Olympic flag that will fly at the games in Sydney in September.
The next ISS module scheduled for launch is a long-delayed Russian service module. This would make the station habitable and ISS managers hope to have the first three-member expeditionary crew in residence by the end of the year.
The shuttle should return to Earth on 29 May.