Yorkshire-born Edmondson raced for Team Colpack in Italy before working with the British U23 Academy at the end of the 2012 season.
The 20-year-old, considered a climbing talent, has been training with Team Sky at their squad camp in Mallorca.
“I’m really excited to be joining Team Sky, and to be taking this next step in my career," Edmondson said. "It’s an amazing set up and a huge project.
"Meeting the team you can see that it is one big unit and that the support you get - with the best coaches and nutritionists in the world - is second to none.
“I see myself as a climbing specialist but my main aim with Team Sky is to develop my tour riding and get used to competing alongside the best riders in the world. I think the first year is a lot about settling in and learning to be part of the team. I’m looking forward to getting to know everyone and further appreciating how to race at this level.”
Team manager Dave Brailsford said: “This is an international team but it’s one with a British heart and we are absolutely committed to nurturing the next generation of British talent.
“We have been keeping an eye on Josh since his time on the Olympic Development Programme and feel he is more than ready to take the next step in his career with a move up to the pro ranks.
"With the coaching and support staff on Team Sky, Josh is in the best possible place to continue his development and we look forward to watching him grow as a rider.”