text: The 50 planes around the world were grounded due to battery malfunctions that saw one 787 catch fire in the US.
  Over the past week teams of Boeing engineers have been fitting new batteries to the aircraft.
  This was after aviation authorities approved the revamped battery design.
  The Ethiopian Airlines plane took off at 09:45 local time (07:45 GMT) and landed in Nairobi, Kenya, some two hours later.
  Each 787 has two of the lithium-ion batteries which caused problems.
  In addition to new versions of the batteries which run at a much cooler temperature, the batteries are now enclosed in stainless steel boxes.
  These boxes have a ventilation pipe that goes directly to the outside of the plane. Boeing says this means than in the unlikely event of any future fire or smoke, it would not affect the rest of the aircraft.
  By Richard WestcottBBC transport correspondent, Nairobi
  Flight ETH 801 between Addis Ababa and Nairobi wasn't exactly a run-of-the-mill flight.
  For starters, it was full of Boeing executives and the boss of Ethiopian Airlines. Several passengers on board asked me what was going on, why was the BBC on a routine flight in Africa?
  Many didn't realise that they were the first passengers to fly in a Dreamliner since it was dramatically grounded in January. There were plenty who knew about the safety scare surrounding the plane, although only a couple that we spoke to said it had made them a little more tentative about flying.
  Boeing still has a huge job on its hands, convincing passengers that its most high-profile, most hi-tech airliner is safe.
  Two senior Boeing executives went out of their way this week to tell me that they'd happily put their family on the plane. It's the kind of quote that sounds good.
  Still, Boeing will be desperately hoping that its Dreamliner nightmare doesn't come back to haunt it.
  Boeing said it put 200,000 engineer hours into fixing the problem, with staff working round the clock.
  On Thursday, the US Federal Aviation Administration issued a formal "air worthiness" directive allowing revamped 787s to fly.
  Japanese airlines, which have been the biggest customers for the new-generation aircraft, are expected to begin test flights on Sunday.
  A total of 300 Boeing engineers, pooled into 10 teams, have in the past week been fitting the new batteries and their containment systems around the world.
  Boeing is expected to complete repairs on all 50 of the grounded Dreamliners by the middle of May.
  In addition to the Dreamliners in service with airlines, Boeing has upgraded the 787s it has continued to make at its factory in Seattle since January.
  The Dreamliner entered service in 2011.  Half of the plane is made from lightweight composite materials, making it more fuel efficient than other planes of the same size.
  The two lithium-ion batteries are not used when the 787 is in flight.
  They are operational when the plane is on the ground and its engines are not turned on, and are used to power the aircraft's brakes and lights.
target: An Ethiopian Airlines 787 Dreamliner has flown from Addis Ababa to Nairobi, the first commercial flight by the Boeing aircraft since all 787s were grounded in January.