The six-and-a-half-hour walk began at 13:55 GMT Sunday, 37 minutes ahead of schedule, and concluded at 20:28 GMT, when the astronauts entered the International Space Station (ISS) and the airlock was re-pressurized.
"They accomplished all of the planned tasks," the source said.
During the mission, the astronauts replaced an empty nitrogen tank for the station's cooling system and deployed protective shields on the huge Japanese Kibo module, which has room to house four astronauts.
They also removed thermal covers from the Japanese lab's 10-meter (33-foot) robotic arm and replaced a surveillance camera which was out of order.
The U.S. Discovery space shuttle docked with the International Space Station on June 2. It is expected to undock from the station on June 11 and land back at Kennedy Space Center in Florida on June 14.
