The 25-year-old, who was born in Ljubljana but has lived in London since 2008, has been granted a UK passport.
The world No 83 will compete under the British flag as soon as he has submitted his new passport details to the ATP Tour.
However, it is not yet certain if he will be able to represent Great Britain in the Davis Cup due to International Tennis Federation (ITF) rules which says no one can compete for more than one country in the competition.
The ITF introduced the change on January 1, this year, which stops players from representing a second nation in the Davis Cup, Fed Cup or Olympic Games.
But Bedene is planning to appeal on the basis that his passport application was lodged before the rule change came into force.
He has previously played for Slovenia in the Davis Cup in 2010, 2011 and 2012.