It is hoped the work will mean the orbiter Atlantis will be ready for a 28 September flight to the International Space Station (ISS).
A shuttle should have visited the platform more than two weeks ago to deliver supplies and continue construction work.
Now a team of engineers has investigated the cracks and has decided on the best way to mend them. This should clear the shuttle fleet to resume flying.
Long time
"We've just completed a thorough review of the team's findings and recommendations, and I am pleased to report to you that - pending the satisfactory completion of welding repairs - we plan to resume shuttle flights by the end of September," said Ron Dittemore, Nasa Space Shuttle Program Manager at the Johnson Space Center, Houston.
"There always will be inherent risks in spaceflight and it's our job to manage those risks appropriately."
Shuttle flights were halted when 11 hairline cracks less than a centimetre in length were found in the hydrogen-fuel lines of all four orbiters.
The cracks were in the metal liners and are thought to have been there for years.
Welding team
Nasa is not sure how the cracks were created but engineers are convinced they do not represent a major danger.
Ron Dittemore said "a Super Bowl of welders" had been assembled to mend the lines.
Atlantis will be the first into the repair shop, followed by Endeavour and then Columbia, which should have made the July flight to the ISS. The remaining shuttle, Discovery, is about to undergo major modifications.
The Atlantis mission to the ISS will take off no earlier than 28 Spetember.